Spillover effects between the stock market and the real economy in a mixed-frequency agent-based macrofinancial model

Kotb, Naira; Brenneisen, Jan-Niklas; Lengnick, Matthias; Proano, Christian; Wohltmann, Hans-Werner Article Spillover effects between the stock market and the real economy in a mixed-frequency agent-based macrofinancial model Journal of Economics and Statistics Provided in Cooperation with: De Gruyter Brill Suggested Citation: Kotb, Naira; Brenneisen, Jan-Niklas; Lengnick, Matthias; Proano, Christian; Wohltmann, Hans-Werner (2024) : Spillover effects between the stock market and the real economy in a mixed-frequency agent-based macrofinancial model, Journal of Economics and Statistics, ISSN 2366-049X, De Gruyter Oldenbourg, Berlin, Vol. 244, Iss. 4, pp. 331-350, https://doi.org/10.1515/jbnst-2024-0017 This Version is available at: https://hdl.handle.net/10419/333287 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Naira Kotb*, Jan-Niklas Brenneisen, Matthias Lengnick, Christian R. Proaño and Hans-Werner Wohltmann Spillover Effects Between the Stock Market and the Real Economy in a Mixed-Frequency Agent-Based Macrofinancial Model https://doi.org/10.1515/jbnst-2024-0017 Received January 13, 2024; accepted September 16, 2024 Abstract: This paper illustrates a behavioral mixed frequency macro-finance model where both real and financial variables are generated on a daily basis. Further, while financial sector data is collected at the same frequency as it is generated (i.e. daily), real data can only be collected on a quarterly basis. Under these circumstances, output and inflation, upon which data is available with a significant delay, become unsuitable as the sole information guide for monetary policy. We suggest that policy makers can deal with this information problem by reacting to the variable on which data is collected on high frequency basis: the stock price. Keywords: new Keynesian model; mixed-frequency macroeconomics; behavioral macroeconomics; optimal monetary policy; macro-finance interaction; heuristic switching; JEL Classification: E44; E52; G01 1 Introduction How much additional stability in the real sector justifies a leaning-against-the-wind monetary policy where the policy rate decisively goes beyond the conventional We would like to thank Philipp Hauber for the excellent research assistance. This article is part of the special issue “Advancing Agent-based Economics”published in the Journal of Economics and Statistics. Access to further articles of this special issue can be obtained at www.degruyter. com/jbnst. *Corresponding author: Naira Kotb, Otto-Friedrich-Universität Bamberg, Bamberg, Germany, E-mail: [email protected]. https://orcid.org/0000-0002-5441-0801 Jan-Niklas Brenneisen, Matthias Lengnick and Hans-Werner Wohltmann, Christian-AlbrechtsUniversität zu Kiel, Kiel, Germany Christian R. Proaño, Otto-Friedrich-Universität Bamberg, Bamberg, Germany Journal of Economics and Statistics 2024; 244(4): 331–350 Open Access. © 2024 the author(s), published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. wisdom and reacts to stock price updates? The baggage of appearing to interfere in the stock market is not light to bear. Furthermore, the literature on whether or not, and to what extent, the policy rate should consider leaning, is not settled. In this paper, we focus on the information provided by stock market updates to the policy making process, proposing that a judicious utilization of this information could yield stability benefits that would otherwise be forfeited if this information were overlooked. The primary aim of this paper is to examine how a monetary policy rule that responds to high-frequency stock price updates, which are correlated with the real sector, affects the macroeconomic and financial stability of an economy. This approach is contrasted with waiting for real data to be collected and published at a slower pace, thereby losing intra-quarter information. More precisely, we illustrate a behavioral mixed frequency macro-finance model where both real and financial variables are generated on daily basis. Further, while financial sector data is collected at the same frequency as it is generated (i.e. daily), real data can only be collected on a quarterly basis. This situation, in which a variable’s evolution through time cannot be observed at all dates it is generated, is known as temporal aggregation. Marcet (1991) explains that temporal aggregation frequently occurs in economics because collecting high-frequency data on certain variables is often prohibitively expensive. However, there is no reason to assume that economic time series are collected at a frequency sufficient to fully capture the movements of the economy. For example, while we typically only have quarterly observations on the gross national product (GNP), it is reasonable to believe that the behaviour of the GNP within a quarter carries relevant information about the structure of the economy, even if this behaviour is unobservable. The problem of (temporal) aggregation is not only relevant to economic questions and applications, but extends to various other fields, including political science (Shellman 2004), health studies (Lindo 2015; Phelps et al. 2018), and (discrete) choice modelling (Basu and Sullivan 2017; Wong, Brownstone, and Bunch 2019). The differentiation between the frequency at which agents make their economic decisions and the frequency at which the information relevant to them becomes available is by no means trivial, as the latter may condition the former. For instance, as we will discuss below, if the policy interest rate set by the monetary authorities is specified as a function of the real gross domestic product (GDP) and price inflation, and the realizations of these two variables become observable on a quarterly basis, the policy rate will adopt that quarterly frequency too, even though in principle it could be reset on any given day. Moreover, the greater the discrepancy between the data generating process (DGP) and the data collection process (DCP), the more significant nowcast and forecast biases will become. 332 N. Kotb et al. In models where agents are boundedly rational and backward-looking, like ours, the discrepancy between the DGP and the DCP is particularly significant. This is due to the dual nature of information and cognitive constraints: on the one hand, these agents must form expectations based on historically available data rather than a model-consistent approach; on the other hand, this data is available to them with a delay due to temporal aggregation. Our paper is closely related to literature where decisions (expectations) are made under cognitive constraints and rely on simple discrete choice models in environments with issues such as data availability, collection delays, or aggregation. Notable examples include the discrete choice approach to environmental and energy decision-making (Grilli and Ferrini 2022) and graph learning (Tomlinson and Benson 2024). The literature most relevant to our paper includes Kontonikas and Ioannidis (2005), Kontonikas and Montagnoli (2006), Bask (2012), Westerhoff(2012), Naimzada and Pireddu (2013), Lengnick and Wohltmann (2013, 2016), Franke and Sacht (2014), and most recently, Proaño and Kotb (2024). Except for the latter, none of these authors, however, models the discrepancy of the DGP and the DCP explicitly. To address this, we modify the theoretical model by Lengnick and Wohltmann (2016) to explicitly differentiate between the DGP and DCP, and study the implications for policy making. In contrast to Proaño and Kotb (2024), who concentrate on analysing real shocks, our focus lies on financial shocks. We investigate how these shocks propagate to the real economy within a framework where real data are temporally aggregated, rendering real variables alone unsuitable for the purpose of highfrequency policy design. The remainder of this paper is organized as follows. Section 2 describes our mixed-frequency behavioural macroeconomic model. Section 3 provides the results of the simulation and the associated analysis. Section 4 concludes. 2 The Theoretical Framework In the following, we set up a behavioural macroeconomic model where all economic activities, both in the financial and the real sectors, take place on a daily basis. Further, we assume that real macroeconomic variables are observable on a quarterly basis given the data collection costs associated with variables such as the GDP and its components in the real world. As we will discuss later, this assumption has important implications since it affects the agents’information sets, and thus their forecasts and economic decisions. To be as clear as possible in our exposition, we use distinct indices that resemble the different frequencies at which economic decisions are made as well as the Mixed-Frequency Agent-Based Model 333 frequencies at which data is collected. The index trefers to the daily frequency in our framework. We denote by qthe quarterly time index. Further, let Tqdenote the number of “trading days”, i.e. days with economic activity, in a quarter. Following Lengnick and Wohltmann (2013, 2016), we assume that there is no economic activity (stock market trading, goods production, etc.) on the weekends, so that Tq= 64 ≈3⋅30 ⋅5 7days per quarter. This implies that a quarter, q,isdefined to contain the days 64(q−1) +1, …,64q. This is illustrated in Figure 1. The upper part of the figure depicts the evolution of the data collection process, which occurs at a quarterly frequency. The lower part shows the evolution of the data generating process, which occurs at a daily frequency. 2.1 The Real Sector To facilitate a better understanding of our high-frequency modelling approach and the role of different information sets at different frequencies, we describe first the quarterly law of motions of the Lengnick and Wohltmann (2016) model. Then we derive the corresponding formulations at the daily frequency following Franke and Sacht (2014). The IS equation derived in Lengnick and Wohltmann (2016) reads xq=E qxq+1 [] −1 σiq−E q[πq+1] [] +c1E qΔsq+1−πq+1 [] (1) where x q represents the output gap, i q the policy nominal interest rate, s q the average stock price, σthe risk aversion coefficient, and E  q[xq+1]and E  q[πq+1] the agents’aggregate output gap and inflation expectations at quarter qconcerning the next quarter q+1, respectively. The tilde denotes that expectations are formed in a boundedly rational way in contrast to the rational expectations operator E t [⋅]. The new Keynesian Phillips curve (NKPC) reads πq=βE q[πq+1]+γxq−κsq(2) Figure 1: Time scale as indexed by trading days (t) and quarters (q). 334 N. Kotb et al. where β=1/(1+r ), where r is the steady state real interest rate in quarterly terms, and γ=(1−θ)(1−βθ)(σ+η) θ, where ηis the inverse Frisch elasticity of labour supply and θ represents the degree of price stickiness (measured at the quarterly frequency). 1 As in Franke and Sacht (2014), we denote now with hthe time interval of a frequency of interest relative to the quarterly time interval (with 0 < h≤1 for time intervals of a higher-than-quarterly frequency). In case of the daily frequency we have h≡1/Tq, such that the daily IS-equation is given by xt=E t[xt+1]−h σit−E t[πt+1] [] +c1E tΔst+1−hπt+1 [] (3) where x t represents the output gap at day t,i t the nominal interest rate in quarterly terms, which may be reset at any day twithin a quarter, s t the stock price (observable at day t), and E t[Δst+1]the average expectation of the stock price change between t and t+1. Note that, following Franke and Sacht (2014), and to maintain consistency in our definitions, the flow variables are uniformly expressed as ‘quarterized’magnitudes. Accordingly, a nominal interest rate i t of value aper quarter means that, in an h-economy, the interest is ha over the period (t,t+h). The same applies for the inflation rate: price inflation from period tto period t+his equal to the product of the quraterized inflation in period t+h(π t+h ) and h. Furthermore, the high frequency representation of the model requires the adjustment of preference parameters with a time dimension. Accordingly, the discount factor βbecomes βd=1 1+hr, the Calvo parameter θd=1−h⋅(1 −θ), 2 and γd=(σ+η)(1−θd)(1−βdθd) θd. These considerations imply for the dynamics of the quarterized daily inflation rate. hπt=βdhE t[πt+1]+γdxt−κst.(4) 2.2 The Data Collection Process As previously mentioned, in our model, while financial variables, such as stock prices, are observable daily, data on real sector variables suchas the aggregate output gap and aggregate price inflation can only feasibly be gathered on a quarterly basis. 1The value of γis obtained by combining the first order condition of the firm problem under Calvo price mechanism, and the households’first order condition. For more clarification, consult Franke and Sacht (2014). 2For instance, if θ= 0.55, it means that 45 % of firms reset their prices each quarter. Calculating for daily resets, θd=1−1 64 ⋅(1−0.55)≈0.993. Thus, about 0.7 % of firms reset their prices daily, as 1 −0. 993 ≈0.007. Mixed-Frequency Agent-Based Model 335 In order to model this non-trivial issue in a stylized manner, we assume that the daily values of real variables are unobservable until the current quarter has ended. Once the quarter is complete, all daily values of the real variables from that period become available to the statistical office. The office then collects these values to compute a quarterly aggregate, which is subsequently made available to the public. DCP : xq≔1 Tq∑ Tqq t=Tq(q−1)+1 xt(5) DCP : πq≔1 Tq∑ Tqq t=Tq(q−1)+1 πt.(6) 2.3 Expectations of the Real Variables Differentiating the data availability of the model variables significantly impacts the information sets available to agents and the expectations they form about future variables based on these information sets. This differentiation is particularly crucial in a framework where agents are assumed to be boundedly rational and where heterogeneity may play a significant role. In the following, we use rules of thumb employed by Lengnick and Wohltmann (2016), adjusting them however to the DCP discussed above, i.e. Targeting expectations : E tar qyq+1=y y∈{x,π}(7) Static expectations : E sta qyq+1=yq−1(8) Extrapolating expectations : E ext qyq+1=yq−1+αyyq−1−yq−2 () (9) with α y > 0. Agents using the first expectational rule-of-thumb (i.e. targeters) simply assume that the variables of interest (xand π) will be at their explicitly announced targets of the central bank (x and π, respectively). Following, De Grauwe and Macchiarelli (2015) and Lengnick and Wohltmann (2016), we normalise these to zero. Agents using the second heuristic (i.e. static) simply assume that the variables of interest will not change in the next quarter. Finally, agents using the third rule (i.e. extrapolators) add to the most recent quarterly value a momentum term. Note that, while the expectations of the targeters remain constant over time, static and extrapolative expectations change only once per quarter when new data is published. 336 N. Kotb et al. The fractions of agents ωy,j qfor the three heuristics j∈{tar, sta, ext} are determined by a discrete choice approach with the intensity of choice parameter ϕ. ωy,j q=exp ϕAy,j q () exp ϕAy,tar q () +exp ϕAy,sta q () +exp ϕAy,ext q () y∈x,π {} .(10) The attractivity Ay,j qof a heuristic jis defined as a geometric sum of past squared expectation errors (c.f. De Grauwe (2010, 2011)). Ay,j q=− yq−1−E j q−2[yq−1] ⎛ ⎝⎞ ⎠2 −ζAy,j q−1y∈x,π, {} (11) where the memory coefficient 0 ≤ζ< 1 determines the speed of agents’forgetting about the past. Market expectations are then given by a weighted average of the three heuristics. E qyq+1=ωy,tar qE y,tar qyq+1+ωy,sta qE y,sta qyq+1+ωy,ext qE y,ext qyq+1.(12) Note that the settings explained above capture the notion that, while the real variables themselves are generated daily, the quarterly nature of the collection and publication process leads to expectations, weights and attractivity values that follow a quarterly frequency (i.e. change only once per quarter). Hence, the subscript qin equations (7)–(12). Figure 2 illustrates the processes of data generation and collection for the real variables. The solid black line represents the true generating process of the variable, which is only observed at specific time points (e.g. the last day of each quarter when data is collected). Various agents employ different rules of thumb to interpret this observed data and form expectations about the future. 2.4 The Financial Sector As in Westerhoff(2008) and Lengnick and Wohltmann (2016), our theoretical framework depicts the financial sector with two types of traders: chartists and fundamentalists. These traders formulate their expectations regarding future stock prices based on the following rules. E C t[st+1]=st−1+kc[st−1−st−2](13) Mixed-Frequency Agent-Based Model 337 E F t[st+1]=st−1+kfsf t−1−st−1 [] (14) where kcand kfare both positive and sf trepresents the agents’perception about the “fundamental”stock price. Since the true fundamental stock price cannot be known with certainty, agents have to form beliefs about it. 3 Following earlier work, 4 we model the agents’perception to be positively correlated with real economic conditions sf t=gx q−1with g≥0.(15) The excess stock demand functions are given by Di t=ℓE i t[st+1]−st () i∈{C,F}.(16) We also allow for a third excess demand function DNT t=0 which prescribes a “no-trading”position in that period. Traders choose between these three different rules according to their respective attractivity which is determined as a function of past profits. Figure 2: Illustration of boundedly rational expectations in a model with daily DGP but quarterly DCP. 3See also De Grauwe and Kaltwasser (2012) and Bernanke and Gertler (2000). 4Consult Lengnick and Wohltmann (2013), Section 2.3 for more details. 338 N. Kotb et al. policy, we can see that the leaning policy minimizes the sharp variations caused by intense switching behaviour. This leads to smoother business cycles of booms and busts for the stock price and inflation. However, this comes at the cost of a slightly more unstable output gap and an extremely variable interest rate. Figure 7 repeats the exercise with a higher value for the stock price shock standard deviation. The results are even more pronounced. A leaning monetary policy minimizes the switching behaviour in the stock market and inflation expectations, leading to smoother cycles in both inflation and the stock price. The output Figure 6: A simulation for 400 quarters (25,600 days). Blue solid line: δ s = 0. Red dotted line: δ s = 18. σ s = 0.01. Mixed-Frequency Agent-Based Model 345 cycles are also slightly more smoothed. However, the interest rate absorbs all of this removed instability. Comparable findings can be derived by examining the impulse responses of the model variables following a one standard deviation stock price shock. 9 Figure 8 shows the results of a positive shock. Figure 9 shows the results of a negative shock. In the first case (second case), the inflation rate reacts slightly negative (positive) as per Figure 7: A simulation for 400 quarters (25,600 days). Blue solid line: δ s = 0. Red dotted line: δ s = 20. σ s = 0.04. 9Appendix A describes how the impulse response functions are computed. 346 N. Kotb et al. equation (4). When the policy rate is leaning, the stock price is instantaneously stabilized, and the switching behaviour is minimized. The balance between fundamental and chartist expectations results in expected stock prices that are only marginally negative (positive). Consequently, output also responds slightly negatively (positively) as described in equation (3). It is noteworthy to mention that the stepped form pattern of the inflation rate and output (blue solid lines) arises from the fact that the most significant changes to these variables occur at the end of each quarter when data is collected and expectations are updated. When the policy rate leans (red dotted lines), this stepped form pattern becomes smoother due to the daily frequency of interest rate impacts on the movement of these variables. Figure 8: Impulse responses to a positive one standard deviation stock price shock under δ s = 0 (blue solid line) and δ s = 18 (red dotted line). Mixed-Frequency Agent-Based Model 347 4 Concluding Remarks “From the point of view of macroeconomic stability, and particularly of equilibrium determinacy, the conventional wisdom appears to be that an explicit response to stock prices is a bad idea”(Airaudo, Nisticó, and Zanna 2015, p. 1274). Airaudo, Nisticó, and Zanna (2015) showed that a policy response to the stock price could be indeed stabilizing, when the real sector and the financial sector are structurally related. We show that such a policy response can be even more justified, when real data is temporally aggregated. Under these circumstances, output and inflation, upon which data is available with a significant delay, become unsuitable as the sole information guide for monetary policy. The policy makers can extract the missing information by considering leaning against the stock price. We demonstrate that a positive response to stock prices can enhance stability in both the real and financial sectors when a structural relationship exists between Figure 9: Impulse responses to a negative one standard deviation stock price shock under δ s = 0 (blue solid line) and δ s = 18 (red dotted line). 348 N. Kotb et al. them. However, this benefit comes with the potential drawback of an unstable and highly variable policy rate. Additionally, under the assumption of bounded rationality, agents switching between different heuristics leads to nonlinear reactions to shocks and more pronounced dynamic spikes, especially as the switching intensifies. Monetary policy can mitigate this effect by reacting contemporaneously to stock price updates, leading to more stable stock prices and a minimized switching behaviour, which in turn results in smoother real and financial cycles. These benefits must be weighed against the costs of variation in the policy rate. Our model is a stylized attempt to capture the information gains of leaning against the wind in an environment of temporal aggregation and boundedly rational behaviour. Further research can provide an econometric basis for this analysis, analyse real shocks, and study models under different real-financial spillover channels than those examined in our model. Appendix A: Impulse Response Analysis To calculate impulse response functions, we follow the steps of the experiment discussed in Lengnick and Wohltmann (2013). These steps are described as follows: 1. Generate model dynamics for one particular random seed. 2. Generate the dynamics again with the same random seed, but with ϵs 129 increased (decreased) by 0.01. In other words, at time t= 129, which is the first day of the third quarter, the value of the stock price shock is higher (lower) than the same shock at the same time in the previous step with an amount 0.01. 3. Calculate the difference between the trajectories of steps 1 and 2 which gives the isolated impact of the additional shock. 4. Repeat steps 1–3 for 500 times. References Airaudo, M., S. Nisticó, and L.-f. Zanna. 2015. “Learning, Monetary Policy, and Asset Prices.”Journal of Money, Credit and Banking 47 (7): 1273–307. Bask, M. 2012. “Asset Price Misalignments and Monetary Policy.”International Journal of Finance & Economics 540. https://doi.org/10.1002/ijfe.450. Basu, A., and S. D. Sullivan. 2017. “Toward a Hedonic Value Framework in Health Care.”Value in Health 20 (2): 261–5. Bernanke, B., and M. Gertler. 2000. Monetary Policy and Asset Price Volatility. Working Paper 7559. National Bureau of Economic Research. https://doi.org/10.3386/w7559 Coibion, O., and Y. Gorodnichenko. 2011. “Monetary Policy, Trend Inflation, and the Great Moderation: An Alternative Interpretation.”American Economic Review 101 (1): 341–70. Mixed-Frequency Agent-Based Model 349 De Grauwe, P. 2010. “The Scientific Foundation of Dynamic Stochastic General Equilibrium (DSGE) Models.”Public Choice 144 (3–4): 413–43. De Grauwe, P. 2011. “Animal Spirits and Monetary Policy.”Economic Theory 47 (2–3): 423–57. De Grauwe, P., and P. Kaltwasser. 2012. “Animal Spirits in the Foreign Exchange Market.”Journal of Economic Dynamics and Control 36: 1176–92. De Grauwe, P., and C. Macchiarelli. 2015. “Animal Spirits and Credit Cycles.”Journal of Economic Dynamics and Control 59 (C): 95–117. Franke, R., and S. Sacht. 2014. “Some Observations on the High-Frequency Versions of a Standard NewKeynesian Model.”Bulletin of Economic Research 66 (1): 72–94. Grilli, G., and S. Ferrini. 2022. “Discrete Choice Modeling in Environmental and Energy Decision-Making: An Introduction to the Special Issue.”Journal of Environmental Planning and Management 65 (7): 1203–9. Kontonikas, A., and C. Ioannidis. 2005. “Should Monetary Policy Respond to Asset Price Misalignments?” Economic Modelling 22: 1105–21. Kontonikas, A., and A. Montagnoli. 2006. “Optimal Monetary Policy and Asset Price Misalignments.” Scottish Journal of Political Economy 53: 636–54. Lengnick, M., and H.-W. Wohltmann. 2013. “Agent-based Financial Markets and New Keynesian Macroeconomics: A Synthesis.”Journal of Economic Interaction and Coordination 8: 1–32. Lengnick, M., and H.-W. Wohltmann. 2016. “Optimal Monetary Policy in a New Keynesian Model with Animal Spirits and Financial Markets.”Journal of Economic Dynamics and Control 64: 148–65. Lindo, J. 2015. “Aggregation and the Estimated Effects of Economic Conditions on Health.”Journal of Health Economics 40 (C): 83–96. Marcet, A. 1991. “Temporal Aggregation of Economic Time Series.”In Rational Expectations Econometrics, edited by L. P. Hansen, and T. J. Sargent, 237–81. San Francisco: Westview Press. Naimzada, A. K., and M. Pireddu. 2013. “Dynamic Behavior of Real and Stock Markets with Varying Degree of Interaction.”DEMS Working Paper 245: 17. Phelps, C., D. Lakdawalla, A. Basu, M. Drummond, A. Towse, and P. Danzon. 2018. “Approaches to Aggregation and Decision Making –A Health Economics Approach: An ISPOR Special Task Force Report [5].”Value in Health 21: 146–54. Proaño, C., and N. Kotb. 2024. Monetary Policy, Stock Prices and Temporal Aggregation in a New Keynesian Model with Behavioural Expectations. University of Bamberg. unpublished manuscript. Shellman, S. M. 2004. “Time Series Intervals and Statistical Inference: The Effects of Temporal Aggregation on Event Data Analysis.”Political Analysis 12 (1): 97–104. Smets, F., and R. Wouters. 2007. “Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach.” The American Economic Review 97 (3): 586–606. Tomlinson, K., and A. R. Benson. 2024. “Graph-Based Methods for Discrete Choice.”Network Science 12 (1): 21–40. Westerhoff, F. 2008. “The Use of Agent-Based Financial Market Models to Test the Effectiveness of Regulatory Policies.”Jahrbücher für Nationalökonomie und Statistik 228: 195–227. Westerhoff, F. 2012. “Interactions between the Real Economy and the Stock Market: A Simple Agent-Based Approach.”Discrete Dynamics in Nature and Society 2012: 1–21. Wong, T., D. Brownstone, and D. S. Bunch. 2019. “Aggregation Biases in Discrete Choice Models.”Journal of Choice Modelling 31: 210–21. 350 N. Kotb et al.