Price and quantity setting in monopolistic competition.

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Faculty of Economics and Business

Master thesis

Price and quantity setting in monopolistic

competition

Author:

Supervisor:

2

nd

Marker:

Wouter Reijngoud

Prof. Dr. Cars H. Hommes

Dr. Domenico Massaro

Master programme:

Econometrics

Track:

Mathematical Economics

Date:

February 21, 2014

Version:

2

nd

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Abstract

This thesis analyzes an experiment in which subjects operated as firms in markets with monopolistic competition, with limited information and production deter-mined in advance. It investigates whether monopolistically competitive market outcomes are reached in these experimental markets, and if so, how. Models for the price and quantity setting strategies of individual firms are estimated, next to models for firms’ expectations of the average market price. Simulations are con-ducted to assess the impact of different price and quantity setting strategies on the aggregate outcomes of the experimental markets. In the simulations, firms are grouped by their estimated pricing strategy. The main conclusion is that aggregate market outcomes converge towards monopolistically competitive outcomes, but do not always reach them, due to the heterogeneity in the price and quantity setting strategies of individual firms.

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CONTENTS i

1 Introduction

A large number of markets can be described by two stylized facts: the firms in the market

act as monopolists and the products they sell are differentiated. Classic examples of these

monopolistically competitive markets include those for beer, airline tickets and toothpaste. As these markets are widespread, it is important to understand how individual firms determine their prices and quantities and whether monopolistically competitive market outcomes are reached.

The theoretical framework for markets with monopolistic competition was introduced by Dixit and Stiglitz (1977) and Blanchard and Kiyotaki (1987), among others. It states that all firms simultaneously and independently choose a price that maximizes their profits. In turn, the market outcomes will converge to the monopolistically competitive market outcome. In order to reach this conclusion, the model assumes that all firms have full information about the market environment in which they operate and use this information to determine the price that maximizes their profits.

However, the assumption of full information may be too restrictive to describe actual markets. For example, firms may not know the exact specification of the demand function for their product, how actions of competitors influence the demand for their product and what kind of actions those competitors undertake. In these cases, it is less clear how firms determine their prices and quantities and if monopolistically competitive market outcomes are reached.

As a consequence, recent research has tried to relax this assumption. On the theoretical side, Tuinstra (2004) uses a monopolistically competitive market model in which firms have limited information about the demand function. He shows that prices converge to the Bertrand-Nash equilibrium, if firms use a price adjustment process in which they estimate the slope of the demand curve. On the experimental side, Davis and Korenok (2011) analyze the effect of nominal shocks in monopolistically competitive markets. Depending on the amount of information available to the participants, average market outcomes converge towards monopolistically competitive ones. However, most research focuses on oligopolies and on price formation, using the

Bertrand-framework, or on quantity formation, applying the Cournot-framework. Experiments with

oligopolistic markets with price competition are conducted by Brown-Kruse et al. (1994), Dufwen-berg and Gneezy (2000), Abbink and Brandts (2005) and Davis (2002), among others. The results indicate that, even with full information, theoretical predictions do not always present an accu-rate description of the aggregate outcomes of experimental markets (Brown-Kruse et al., 1994).

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1 Introduction 2

Theoretical predictions are also not accurate without full information (Abbink and Brandts, 2005). Furthermore, average prices of individual markets may substantially differ from equi-librium outcomes (Davis, 2002). In addition, increasing the number of firms in experimental markets leads to outcomes closer to equilibrium values (Dufwenberg and Gneezy, 2000).

Experiments with quantity competition in oligopolies are also conducted extensively; an overview is presented by Huck et al. (2004). The authors also study the impact of the number of firms in an experimental market on the average market quantity. They find that outcomes are close to the Cournot prediction if the number of firms increases, as was the case for the market price in the Bertrand-framework. Offerman et al. (2002) analyze the influence of different information sets on the experimental outcomes in Cournot games. Depending on the information set, quantities converge towards the Cournot prediction.

On the other hand, the price and quantity formation processes are rarely analyzed simul-taneously. Mestelman and Welland (1988) analyze posted price and double auction markets with and without production set in advance. Results for both cases are quite similar: after 15 rounds market outcomes are quite close to the Walrasian equilibrium. More recently, Brandts and Guillen (2007) have conducted duopoly and triopoly experiments in which subjects had to decide on their price and their production before each round of the experiment. Most markets end up at monopoly outcomes, as bankruptcy is possible and does occur, or collusive outcomes. This thesis will add to this research by analyzing part of the outcomes of a laboratory exper-iment, conducted by Assenza et al. (2013a), on price and quantity formation under monopolistic competition. Subjects (from here on referred to as firms) act as firms and are asked to submit a price, a quantity to produce and a forecast of the market price in each period under different limited information sets. Allowing firms to choose prices and quantities makes the experimen-tal markets more closely resemble actual markets with monopolistic competition and thus, will increase our understanding of the workings of firms that operate in such markets.

The experiment has two important novel features. First of all, although firms do have some qualitative information about the market environment, they do not have quantitative informa-tion. Hence, firms in this experiment have limited information, as opposed to the benchmark of full information. Second, production is not determined by the demand function, but firms have to set production in advance. Although experiments with advance production have been con-ducted before, this experiment is the first to do this in a market with monopolistic competition

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and limited information.

The main objective of this thesis is to understand whether monopolistically competitive market outcomes are reached in experimental markets, with limited information and production set in advance, and if so, how. To be able to fully understand the mechanisms that determine the aggregate market outcomes, the following subquestions are also investigated. Which price and quantity setting strategies do firms use? Is the formation of prices and quantities homogeneous or heterogeneous? Do firms use different strategies for price and quantity setting with different information sets? Do firms use their expectation of the average market price in their price and quantity setting strategies? Which forecasting rule(s) for the average market price do firms use? And last, what is the impact of different price and quantity setting strategies on aggregate market outcomes?

The remainder of this thesis is organized as follows. Section 2 describes the experimental design and the different treatments in more detail and discusses the experimental results. Sec-tion 3 analyzes the strategies used by firms to determine their price, their quantity and their forecast of the average market price. Models for these strategies are introduced and the es-timation results are discussed. In section 4, 40-periods ahead simulations of the experiment are presented, explaining the impact of different strategies on the aggregate market outcomes. Section 5 concludes.

2 The price and quantity setting experiment

Section 2.1 explains the experiment: section 2.1.1 discusses the monopolistically competitive market environment, which is used in the experiment; the two treatments are introduced in sec-tion 2.1.2; secsec-tion 2.1.3 describes the experimental outline. Secsec-tion 2.2 discusses the experimental results.

2.1 The experimental setting

A brief description of the experiment is presented in this section. This summary is an adaptation

of Assenza et al. (2013a). A full overview of the experimental design and all the different

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2.1.1 The monopolistically competitive market environment

The market environment used in the experiment is a variant of the monopolistically competitive market structure, as introduced by e.g., Dixit and Stiglitz (1977) and Blanchard and Kiyotaki (1987). Demand in each period is linear and given by

qi,t= α − βpi,t+ θpt (1)

where qi,t is the differentiated product of firm i in period t, pi,t is the price firm i charges in

period t and p_t is the average market price in period t. In addition, α > 0, β > θ/n > 0.

These restrictions ensure that the demand line has a negative slope in the firm’s own price and a positive slope in the average market price.

In this thesis I consider four benchmark predictions for the outcomes of the experiment. The first one is the standard monopolistically competitive outcome, which is the results of simul-taneous profit maximization by firms that set their prices independently of other firms. The second benchmark is the Nash equilibrium, in which firms maximize profits based on their best response to the prices of other firms (i.e. the average market price). The last two benchmarks are the Walrasian outcome, where the equilibrium price equals marginal costs, and the collusive outcome, in which firms maximize joint profits.

The parameters in each session (from here on referred to as markets) are fixed at α = 10.5, β = 1.75, θ = 1.45833 and c = 8. Table 1 compares the resulting market prices and average quantities for the four benchmark predictions.

Outcome Market price Ave. quantity

Monopolistic competition 12 7

Nash 12.3 6.9

Walrasian 8 8.17

Collusion 22 4

Table 1: Theoretical benchmarks.

2.1.2 The two treatments

The experiment is divided into three treatments. This thesis analyzes markets of two treatments and hence, this section only discusses those two.

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In the first treatment all firms know their own price, the average market price, their quantities, their sales and their profits up to and including period t−1. Firms also observe their excess supply, that is quantity produced minus sales. In each period t, firms can use this information to set their price and determine their production level. In addition, each firm also submits a forecast of the average market price. Assenza et al. (2013a) expect that this variable is important in deciding both how much to produce and at which price to sell, for firms that try to incorporate the prices of other firms in their own pricing strategies. The only information that those firms have about the prices of other firms are the past observed average market prices. Hence, they might use their forecast of the average market price for the current period in their pricing strategies.

In the second treatment, all firms have to decide upon the same three variables: the price they set, the quantity they produce and a forecast of the average market price. The difference between the first and the second treatment is the extension of the information set. In period t firms also observe excess demand, next to excess supply, up to and including period t − 1. The excess demand is the ’potential’ demand given the price they set and the average market price. The difference between treatment 1 and treatment 2 makes it possible to asses the impact of different information sets and, ultimately, different market structures on the aggregate market outcomes and price and quantity setting strategies of individual firms.

2.1.3 The experimental outline

The actual experiment consists of 11 markets. This thesis analyzes four of those: market 2 and 4 of treatment 1 and market 1 and 2 of treatment 2.

The experiment took place in series of 20- and 30-participants sessions. Subjects were not informed about the number of firms in each market. In the beginning of each session, experi-mental instructions were handed out, that informed participants about their role as firms. In each of the 50 periods, they had to set a price between 0 and 30 and simultaneously decided upon a quantity to produce between 0 and 40. The instructions also included qualitative, but no quantitative information about the market environment. After the end of the experiment, participants were asked to fill in a questionnaire about their actions during the experiment.

Payments to the participants were based on the cumulated profits at the end of the ex-periment. Experimental Count Units (ECU) were used as substitute for money. The cost of producing one unit is constant at 8 ECU. The participants started with an initial balance of 500 EUC to accommodate possible losses. To encourage subjects to give reliable forecasts of

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the average market price, they were rewarded with 0.10e, if their forecast lay within 1 ECU of

the realized market price in that period. Otherwise the reward was zero. Total payments were the sum of the earnings from the forecasting game plus the market earnings at the end of the

experiment at a rate of 75 ECU = 1e.

2.2 The experimental results

This section describes the experimental results for markets 2 and 41_{of treatment 1 and markets}

1 and 2 of treatment 2. Table 2 presents the means and standard deviations of the average market prices and quantities for the periods 11 to 30 and for periods 31 to 50. The first 10 periods are removed from the sample to exclude possible learning effects.

Treatment 1 Treatment 2

Market 2 Market 4 Market 1 Market 2

Periods price quantity price quantity price quantity price quantity

11-30 10.376 7.259 10.111 7.602 10.538 7.246 13.144 6.812

(0.663) (1.404) (0.547) (2.268) (0.485) (1.883) (0.864) (1.382)

31-50 11.603 7.078 10.998 7.465 11.175 7.278 12.647 6.833

(0.391) (1.937) (0.269) (2.062) (0.256) (1.209) (0.226) (1.129)

Table 2: Average prices and quantities of each market for rounds 11 to 30 and 31 to 50 (standard deviations in parentheses).

Observation 1. The average market prices stay slightly above or below the monopolistically competitive price, despite a converging trend. The average market prices for the last twenty periods of market 2 and 4 of treatment 1 are 11.603 and 10.998, respectively. This is below the

monopolistically competitive market price (pM C) of 12. The differences between the experimental

market prices and pM C _{are significant as indicated by a Mann-Whitney U-test at p-values of 0.00.}

The results for both markets of treatment 2 are similar: average market prices are 11.175 and 12.647 in the last twenty periods of the experimental market. The differences between these

prices and pM C _{are again significant at p-values of 0.00.}

Hence, of the four benchmark predictions, the monopolistically competitive market price comes closest to three of the four experimental market prices. However, for market 2 of treat-ment 2 the average market price in the last twenty periods is closer to the Nash equilibrium,

1_{Two firms have been deleted from the sample of market 4 as they went bankrupt in the first 10 periods of}

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as pN E _{= 12.3, although the difference between both prices is significant as indicated by a}

Mann-Whitney U-test at a p-value of 0.00. That the average market price is closer to the Nash equilibrium can be explained in several ways. First of all, both equilibrium prices are quite close to each other. Second, due to the limited number of firms in the experimental market, firms might try to incorporate the pricing strategies of other firms into their own instead of acting as a monopolist. These type of strategies are actually a feature of the Nash equilibrium and therefore, outcomes might be closer to that equilibrium.

0 10 20 30 40 50 0 5 10 15 20 25 period price Treatment 1, market 2

average market price

0 10 20 30 40 50 0 5 10 15 20 25 period quantity Treatment 1, market 2 average quantity 0 10 20 30 40 50 0 5 10 15 20 25 period quantity Treatment 1, market 4 average quantity

Figure 1: Experimental results for treatment 1. Left panels: market 2. Right panels: market 4. Thick blue line: average market price; thick red line: average market quantity; dashed line: monopolistically competitive market price (upper panels) or quantity (lower panels); thin lines: price (upper panels) or quantity (lower panels) of individual firms.

At the same time, average market prices show a converging trend. For all four markets, the average market prices in the last twenty periods are closer to the monopolistically competitive outcome than in periods 11 to 30. A Wilcoxon signed rank test confirmed that the average prices

in the last 20 periods are significantly closer to pM C at p-values of 0.00 for all four markets.

Observation 2. Average market quantities converge towards the monopolistically competitive market quantity in the first rounds of the experimental markets. This is most easily seen from the lower panels of figures 1 and 2. For both treatments, the average market quantity is close

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to the monopolistically competitive market quantity (qM C_{) of 7 after the first 10 periods of the}

experimental markets. However, the average market quantity is still significantly different from

qM C _{as indicated by a Mann-Whitney U-test at p-values of 0.00.}

The convergence is clearly in the first 10 periods of the experiment. Thereafter, the average market quantities do not display a converging trend, although the market quantities in all but

one market are closer to qM C in the last twenty periods of the experiment than in periods 11 to

30. However, these differences are not significant as indicated by a Wilcoxon signed rank test at p-values larger than 0.38.

0 10 20 30 40 50 0 5 10 15 20 25 period quantity Treatment 2, market 1 average quantity 0 10 20 30 40 50 0 5 10 15 20 25 period quantity Treatment 2, market 2 average quantity

Figure 2: Experimental results for treatment 2. Left panels: market 1. Right panels: market 2. Thick blue line: average market price; thick red line: average market quantity; dashed line: monopolistically competitive market price (upper panels) or quantity (lower panels); thin lines: price (upper panels) or quantity (lower panels) of individual firms.

Furthermore, extending the information set with the excess demand leads to average market

quantities closer to qM C. Table 3 shows the mean squared error (MSE) between the average

market prices and quantities and the monopolistically competitive market outcome. The MSE for the average quantity decreases in treatment 2 compared to treatment 1 with roughly a factor two.

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2 The price and quantity setting experiment 9 MSE price quantity Treatment 1 market 2 2.297 4.226 market 4 3.468 4.321 Treatment 2 market 1 2.072 1.798 market 2 2.048 2.295

Table 3: Mean squared error (MSE) between the average market price and quantity and the monopolistically competitive market outcome.

competitive market outcome, but quantities of individual firms are not converging. That prices converge can be seen from the upper panels of figures 1 and 2: prices of individual firms show large oscillations in the first 10 periods, but converge afterwards. A possible cause of this convergence might be that firms use the past observed market price as an anchor when they determine their

price: the market price converges towards pM C and hence, the prices of individual firms that use

the past observed market price as an anchor converge too.

Quantities of individual firms do not seem to be converging towards qM C_{. Even after the}

first 10 periods firms show a large variability in the quantities they set, as can be seen from the lower panels of figures 1 and 2. Extending the information set with the excess demand seems to reduce this variability, as the amplitude of the oscillations of the quantities of individual firms are smaller in treatment 2 compared to 1.

In addition, the price and quantity setting strategies seem to be heterogeneous. Different firms use different strategies: the prices and quantities of some firms cross the average market price or quantity multiple times, while others firms keep their prices and quantities almost consistently above or below the average market price. There are also firms that keep their price relatively constant. This is the case in treatment 1, as well as in treatment 2.

Thus, aggregate market outcomes and the prices that individual firms set are converging towards the monopolistically competitive outcomes in the experimental markets, but do not reach them. Note that firms in these markets have limited information about the market environment and have to set production in advance. Average market quantities converge faster than prices, while firms show a large variability in the quantities they set during the whole experiment. In addi-tion, the average market prices and quantities in the experiment are not close to the remaining

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benchmarks, i.e. the Walrasian and the collusive benchmark.

Part of these experimental results have been reported in earlier research. However, as men-tioned before, most research has focused on price or quantity setting instead of both. With respect to aggregate market prices, Huck et al. (2000) and Davis (2002) also find that they do not fully converge to the theoretical benchmark for oligopolistic market environments. Davis and Korenok (2011) confirm this for monopolistically competitive markets, but it depends on the treatment and they focus on the effect of nominal shocks on market outcomes instead of price and quantity formation.

Aggregate market quantities above their equilibrium values are also found in Huck et al.

(2004) and Bosch-Dom`enech and Vriend (2003), among others. Huck et al. (2004) analyze how

the number of firms affects the outcomes of experimental Cournot markets in which subjects have full information. For markets with more than three firms, average quantities are different

from the Cournot prediction. Bosch-Dom`enech and Vriend (2003) confirm this for markets with

two or three firms.

Brandts and Guillen (2007) do analyze experiments in which subjects set prices and quantities and their results confirm the results in this section. They also find the aggregate outcomes of duopolies and tripolies are converging towards the Cournot equilibrium, but the outcomes do not reach it.

In addition, the observation that collusion does not occur in the experimental markets is not surprising. Huck et al. (2000) state that collusion rarely occurs in markets with more than three firms, while the markets in this experiment have ten firms.

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3 Firm-specific models for price and quantity setting 11

3 Firm-specific models for price and quantity setting

Section 3.1 introduces models for the three decision variables. The estimation method is explained in section 3.2. Section 3.3 discusses the estimation results.

3.1 Firm-specific models

The following models for the three decision variables are estimated for all firms:

pe_i,t = c + δ1pt−1+ δ2∆p + δ3pei,t−1+ εi,t (2)

pi,t = c + β1pi,t−1+ β2pei,t+ β3[±(∆πi)] + β4∆pi+ β5[±(∆πi)∆pi] + β6Si,t−1+ νi,t (3)

qi,t = c + γ1qi,t−1+ γ2pi,t+ γ3pei,t+ γ4Si,t−1+ µi,t (4)

where pe

i,tstands for firm i’s expectation of the average market price in period t, pi,tfor the price

of firm i in period t and qi,t for the quantity that firm i produces in period t.

The expectation of the average market price of firm i in period t in model 2 is explained by

the one period lag of the average market price, p_t−1, firm i’s expectation of that price in period

t − 1, pe_i,t−1 and the change in the average market price, ∆p. This specification is based on the

findings of Assenza et al. (2013b).

The price of firm i in period t in model 3 is explained by its one period lag pi,t−1, the excess

supply in period t − 1, Si,t−1, and the firm’s expectation of the average market price in period

t, pei,t. The last variable is included to see whether firms use this forecast as an anchor in their

price setting strategies. This could be the case, because the experimental results show that some firms are using anchoring strategies, i.e. staying consistently above or below the average market price (see observation 3). In addition, the answers on the questionnaires that were handed out after the experiment also support the hypothesis of anchoring: subjects wrote that they use the average market price as an anchor to determine their prices.

The variable ±(∆πi)∆pi is also part of the model. This variable is the change in price times

the sign of the change in profits from period t − 2 to t − 1 for firm i. For example, if firm i

increases the price with 2 in period t − 2 to t − 1 and the change in profits is -10, ±(∆πi)∆pihas

a value of -2.2 This variable is included to test whether firms use the interaction between their

2_{Models with ∆π}

i∆pi have also been estimated. However, models with ±(∆πi)∆pi are more informative

because they indicate in which direction prices have to go to increase profits. This is also indicated by ∆πi∆pi,

but in a more exact way, which is less realistic for firms in this experiment. Estimation results (not shown in this

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prices and the resulting profits in their pricing strategies.3 _{As such, it measures the ‘feedback’}

of profits on the price firms set and therefore, it is referred to as the profit feedback variable in this thesis. The individual parts of the interaction term have no clear economic interpretation,

but they are included for econometric reasons.4 Hence, they are excluded from the model if the

profit feedback variable is not significant.

Model 4 explains the quantity firm i produces in period t. Explanatory variables are its one

period lag qi,t−1, the price of firm i in period t, firm i’s expectation of the average market price

in period t and the one period lag of the excess supply, Si,t−1. This model is estimated because

it nests the actual demand function and allows for a comparison between the treatments due to

the inclusion of Si,t−1.

3.2 Estimation procedure

The estimation procedure starts with the addition of dummy variables for outliers to the dataset and the removal of a learning phase. Including dummy variables is necessary, as some firms

changed pe

i,t, pi,tor qi,t dramatically in one period and reversed this in the next period. Without

the extension of the dataset with dummies for the resulting outliers as additional explanatory variables, the estimated coefficients would be biased. An outlier is defined as an observation that

differs more than three standard errors from the average observation.5 _{In addition, a learning}

phase, that consists of the first 10 periods of the experimental markets, is removed from the regression sample. This prevents that the period in which firms form their strategy to determine pei,t, pi,t and qi,t, influences the regression results

The model for pei,t is estimated by ordinary least squares (OLS). Insignificant coefficients

are removed iteratively, coefficients with the highest p-value first. Standard diagnostic test for

heteroskedasticity and autocorrelation are used to evaluate the estimation output.6 _{If the tests}

indicate the presence of either heteroskedasticity or autocorrelation, the standard errors and p-values are adjusted accordingly, using respectively the heteroskedasticity corrected standard

3_{The profit feedback variable does not always give the right advice, because it is only an approximation of}

the partial derivative of the profit function with respect to pi,t−1. However, including the partial derivative is

not realistic because firms have only qualitative and no quantitative information about the market. It is also not feasible because it leads to multicollinearity problems. Models with a closer approximation of the partial

derivative than ±(∆πi)∆pi have also been estimated and they confirmed the intuition above: the variable was

not significant at the 5% level for almost all firms.

4_{Not including these individual terms makes the estimation results no longer invariant to location shifts, for}

example if the individual terms are centered by their means (Peixoto, 1990).

5_{Dummy variables consist of a 1 in period t of the outlier and 0’s otherwise.}

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errors of White (1980) or heteroskedasticity and autocorrelation corrected (HAC) standard errors

of Newey and West (1987).7

Estimating the models for pi,t and qi,t is somewhat more complicated due to possible

endo-geneity in the explanatory variables. As pe_i,t, pi,t and qi,t are simultaneously determined, they

could possibly be endogenous8when used as explanatory variables in models 2 to 4. Model 3 has

one possible endogenous explanatory variable, pei,t and model 4 has two, pei,t and pi,t. There are

no possible endogenous variables in model 2. It can be argued that pi,t should also be included

in model 2, because firms may try to influence the average market price in period t by increasing or decreasing their price in that period. In turn, this would influence their expectation of the average market price in period t. However, as explained in section 2.1.3, during the experiment 20 or 30 participants, that were acting as firms, were sitting in the same room and they knew neither the number of firms in their market nor the fact that more markets were taking place at the same time. Therefore, it is most likely that the participants concluded that everyone was active in the same market and that their influence on the average market price was small. Hence,

pi,t is not included as explanatory variable in model 2.

To test for possible endogeneity the Hausman test is used (Hausman, 1978). This is straight-forward with homoskedastic errors, but the errors are possibly heteroskedastic or autocorrelated. A solution would be to use HAC standard errors when calculating the test statistic, which asymp-totically should be equivalent to the Hausman test (Davidson and MacKinnon, 1993, p. 239). However, in small samples like the one used in this experiment (for every firm the number of observations (N ) is 50) this approach can lead to large size distortions (Andrews (1991) and Andrews and Monahan (1992)). To counteract this problem the method of Kiefer et al. (2000) is used to calculate the F statistic for the Hausman test, when the errors exhibit heteroskedasticity or autocorrelation. This method is useful because the test statistic Kiefer et al. (2000) propose is calculated as

F_haus∗ = T (R ˆβ − r)0[R ˆBR0]−1(R ˆβ − r)/q (5)

Instead of using a HAC estimate of the variance-covariance matrix, as is the case for the classic F

test, ˆB is used. ˆB does not require a HAC estimate of the variance-covariance matrix. Therefore,

7_{A small sample size correction is applied when the HC or HAC standard errors are calculated. Other methods,}

that correct for small sample size, like prewithening (Andrews and Monahan, 1992) or the method of Kiefer et al. (2000) have also been implemented, but the differences in the estimation results were minor: in only 1/6 of the models the estimation results changed and these changes were small. Thus, the standard method is used.

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the test statistic F_haus∗ has better finite sample size properties.

Instrumental variables (IV) methods are applied when the Hausman test rejects the null

hy-pothesis of exogeneity. The two stage least squares estimator is used to estimate the coefficients.9

Insignificant coefficients are removed iteratively, coefficients with the highest p-value first. The

significant regressors from the estimation of model 2 are used as instruments for pei,t in the

esti-mation of models 3 and 4. Significant regressors cannot be used as instruments in the estiesti-mation of respectively model 3 or 4, if they are also included as explanatory variables in model 3 or 4. If this holds for all significant regressors, there will not be any instruments. In that case, the

insignificant regressors of model 2 are used as instruments for pe

i,t. Similarly, significant

regres-sors from the estimation of model 3 serve as instruments for pi,t in the estimation of model 4.

If all significant regressors are included as explanatory variables in model 4, the insignificant

regressors from the estimation of model 3 are used as instruments for pi,t.10 To test for weak

instruments, the first stage F statistic is calculated. The test of Sargan (1958) is used to identify possible instrument endogeneity.

The test of White (1980) is used to test for heteroskedasticity. Using this test for IV regres-sions can results in an invalid test statistic, when the assumption of homoskedastic errors in the first stage regression is violated, as shown by Pagan and Hall (1983). They propose a test for heteroskedasticity which relaxes this assumption. However, Pesaran and Taylor (1999) indicate that the Pagan and Hall statistic rejects too often in small samples, whereas the White test does not. Therefore, the standard White test is used, due to the small sample size. To test for auto-correlation the Sargan (1988) test is applied, which is a generalization of the Breusch-Godfrey test for IV regressions. If the tests indicate misspecification, the standard errors and p-values are

adjusted accordingly.11 Finally, the standard R2 measure can be misleading for IV regressions,

as pointed out by Pesaran and Smith (1994). To correct for this possibility a generalized version

of R2 is constructed, which uses the errors of the second stage regression of the 2SLS method

(Pesaran and Smith, 1994).

9_{For an explanation of this method, see Cameron and Trivedi (2005) and Verbeek (2008), among others.}

10_{In some cases the instrument set was slightly altered to prevent weak instruments or exogeneity problems.}

The instruments used in the estimations with IV can be found in tables 18 and 19 in appendix B.

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3.3 Estimation results

The results are shown in tables 6 to 17 in appendix A. As estimation method, OLS is used most

frequently. However, for some firms the models for pei,t or pi,t are estimated with IV methods.

Appendix B presents an overview of the instruments used to estimate those models and the first stage F and Sargan statistics. As can be seen from the last two columns in table 18 and the last three columns in table 19, the instruments are exogenous and for all but one firm, there is no weak instrument problem.

In general, the results indicate that models 2 to 4 present an accurate description of the variation in the three decision variables. For all but one firm, the models describe the strategies

that the firms apply to determine the decision variables.12 _{Furthermore, the signs of the majority}

of the coefficients are as expected and the tests on autocorrelation and heteroskedasticity do not reject their null hypotheses for most firms.

Observation 4. Individual forecasting heuristics for the average market price are equal to well-known forecasting strategies. The forecasting heuristics of 95% of the firms can be divided into four categories: naive, anchoring and adjustment, adaptive and trend following. The largest category consists of 11 firms for which only the past observed average market price (and possibly the constant) is significant and hence, these firms use naive expectations. Ten firms, that have significant coefficients for the last three variables in model 2, make up the second largest category. Their strategies can be described as a simplified version of an anchoring and adjustment heuristic, with the combination of both past observed prices as the anchoring part and ∆p as the adjustment part. The third category consists of eight firms for which both past observed prices are significant and hence, they use adaptive expectations. Seven firms make up the final category of trend

followers, because they have significant coefficients for p_t−1and ∆p.

In addition, these results are generally consistent across treatments. The four forecasting heuristics are used in both treatments. This was to be expected, as the addition of the excess demand to the information set in treatment 2 is not relevant for the forecast of the average market price. Of course, there are some minor differences. Most importantly, eight out of the ten firms that use the anchoring and adjustment heuristic are part of treatment 2.

12_{In market 1 of treatment 2 model 3 does not describe firm 10’s strategy for p}

i,t, because the only significant

variable is the constant. If firm 10 kept its price constant during the experiment, the model would describe firm 10’s pricing strategy. However, a plot of firm 10’s price (not shown in this thesis) reveals that it fluctuates during the experiment.

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Observation 5. Firms use the expected market price as anchor in their pricing strategy and deviations from this anchor are often related to past observed excess supply or past realised profits. Individual forecasts of the average market price are significant for 55% of the firms. Hence, firms use this forecast as an anchor. Most firms extend this anchor with the price they have set in the last period: the past individual price is significant for 89% of firms.

0 10 20 30 40 50 7 8 9 10 11 12 13 14 15 period price Treatment 1, market 4

average market price price firm 6 forecast firm 6 0 10 20 30 40 50 7 8 9 10 11 12 13 14 15 period price Treatment 2, market 1

average market price price firm 5 forecast firm 5

Figure 3: Illustration of anchoring. The dashed line indicates the forecast of the average market price of the individual firm.

Figure 3 graphically illustrates the use of the expected market price as an anchor for both treatments. As can be seen from the left panel, firm 6 in market 4 of treatment 1 consistently stays below its forecast of the average market price, besides from period 29 where the forecast is lower than the price of firm 6. The right panel illustrates anchoring for firm 5 in treatment 2, market 1. Firm 5 stays slightly above its forecast of the average market price from period 14 onwards.

Next to the anchor, a majority of firms, 64%, uses an adjustment mechanism in their pricing decisions. As adjustment mechanism either the past observed excess supply, past observed profits (i.e. the profit feedback variable) or a combination of both can be used. Of all firms that use one of these adjustment mechanisms, the past observed excess supply is used by most firms, 63%. Past observed profits are used by 30% and the combination by 7%.

Hence, past observed excess supply is used more often as adjustment mechanism than past observed profits. As the goal of the firms in the experimental markets is profit maximization, one would expect past observed profits to appear more often. However, past observed excess supply is directly available to the firms, while the profit feedback variable has to be calculated. This extra effort possibly prevents firms from using it. Furthermore, the presence of firms that use an anchoring strategy, i.e. consistently staying above or below the average market price as

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de-3 Firm-specific models for price and quantity setting 17

scribed in observation 3, may also lead to smart firms that discard the profit feedback variable. For example, anchoring firms might keep the average market price below its monopolistically competitive market equilibrium. If the profit feedback variable then indicates that a price in-crease raises profits, firms using that variable possibly overshoot: they inin-crease prices too much compared to the average market price and hence, sales decrease and in turn, profits. Smart firms might understand this and thus discard the profit feedback variable.

In addition, past observed profits are used mostly by firms in treatment 2, while firms that use past observed excess supply are equally divided between the two treatments. Of all firms that use past observed profits, 78% are part of treatment 2, while this only holds for 53% of firms that use past observed excess supply (and demand). Hence, the extension of the information set

with excess demand does not result in an increase of the use of past observed excess supply13_,

but to an increase in the use of past observed profits.

Observation 6. The quantities firms set clearly depend negatively on individual pricing deci-sions and positively on the expected market price and they are adjusted adaptively to eliminate past observed excess supply or demand. The significant coefficients for the individual prices are negative for all but three firms. The significant coefficients for the expected market price are all positive, except for firms for which the individual price is not significant. Those firms use their expectations of the market price as substitute for their individual prices and hence, the coefficients are negative. Furthermore, even without quantitative information about the market environment, nine firms are able to replicate the actual demand function 1, as only the constant, the individual price and the expected market price are significant in their quantity setting strate-gies. Next to this, quantities are adjusted adaptively to eliminate excess supply or demand. This is done by 37% of the firms for which past observed excess supply is significant.

Comparing both treatments shows that past observed excess supply is significant for (almost) the same percentage of firms in both treatments: 39% in treatment 1, 35% in treatment 2. One would expect this variable to appear more often in the estimation results for treatment 2, because the extension of the information set with excess demand gives firms valuable extra information about the demand function that can be used to optimize profits. However, firms seem to use this information, as the average profit in the two markets of treatment 1 is 542 ECU, while being

906 ECU in treatment 2.14 _{This difference is significant as indicated by a Mann-Whitney U-test}

13_{Note that extending the information set with excess demand means that excess supply can also become}

negative.

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at a p-value of 0.00.

A way to explain this anomaly, i.e. that firms in treatment 2 have significantly higher profits, while they do not seem to use the extension of information set, comes from the observation that excess supply for firms in treatment 2 is closer to zero. Average excess supply in treatment 1 is 17.2, while -0.9 in treatment 2. This difference is significant as indicated by a Mann-Whitney U-test at a p-value of 0.00. Hence, firms learn to minimize excess supply in treatment 2 in the learning phase, after which the excess supply is close to zero. As variables that are close to zero are not very likely to be significant, excess supply will not be significant for more firms in treatment 2 than in 1.

Observation 7. There is clear evidence for heterogeneity in the strategies for the three decision

variables. For each of these three variables, firms apply a number of different strategies. For pe_i,t

5 strategies are used, for pi,t 10 and for qi,t no less than 12. Some of these strategies are used

by one firm only, but for each decision variable there are at least four strategies used by at least three firms. Hence, the estimation results confirm the graphical observation 3 that strategies of the individual firms are heterogeneous.

Next to the heterogeneity in the strategies for each of the decision variables, there is also heterogeneity between the firms that use the same strategy for one of the decision variables. For example, firms that use the same strategy in their pricing decisions, do not necessarily use the same quantity setting strategy or forecasting heuristic for the average market price.

In addition, heterogeneity occurs independently of the treatment. However, it increases

slightly when the information set is extended in treatment 2. This holds especially for the

quantity setting strategies.

Thus, the estimation results indicate that strategies for the three decision variables in markets with limited information and production set in advance, are heterogeneous. Firms use well-known forecasting heuristics to form an expectation of the average market price. In their pricing decisions firms use this expectation as an anchor and past observed excess supply or profits are used as adjustment mechanism. Production decisions depend negatively on individual pricing decisions and positively on the expected market price and are adjusted to eliminate past observed excess supply.

Earlier research, whose outcomes can be compared with the estimation results, is limited. excluded from the profits of each firm. Firms 4 and 8 of treatment 1, market 4, are not part of the sample, as they went bankrupt.

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4 40-periods ahead simulations 19

The anchoring observed in the individual forecasting heuristics and the price setting strategies

was first described by Tversky and Kahneman (1974). They introduced the anchoring and

adjustment heuristic to explain individual decision making under uncertainty. Furthermore,

three of the four observed individual forecasting heuristics were also used by participants in the experiments of Assenza et al. (2013b), namely the adaptive, trend following and anchoring and adjustment heuristics. Finally, Davis and Korenok (2011) also find evidence for anchoring in their experiments: subjects use their best response actions only occasionally and seem to anchor their pricing decision to those of their competitors.

The heterogeneity described in observation 7 for the individual forecasting heuristics has also some predecessors. The forecasting strategies of participants in Assenza et al. (2013b) are also heterogeneous. In addition, heterogeneous expectations have been incorporated in theoretical modeling, as in Massaro (2013). However, to my knowledge this thesis is the first to analyze heterogeneity in the price and quantity setting strategies of firms in monopolistically competitive markets with limited information.

4 40-periods ahead simulations

This section presents the 40-periods ahead simulations of the experimental markets. Section 4.1 explains the simulation procedure. Section 4.2 discusses the results of the simulations.

4.1 Simulation procedure

The main objective of the 40-periods ahead simulations is to understand the impact of the different strategies employed by firms on the aggregate outcomes of the experimental markets. In order to do so, firms are grouped by their price-setting strategy. Firms are not grouped by their strategies for the other two decision variables, because strategically those are not the most

important ones.15 The number of groups is limited to three. This limit is set in order to keep

the number of firms per group in most markets above one.

The three groups consist of profit seekers, quantity adjusters and adjusters. Profit seekers are firms that only use past observed profits as adjustment mechanism in their pricing strategy; they have a significant coefficient for the profit feedback variable in model 3. Quantity adjusters

15_{The price is the main strategic variable, because the price a firm sets, determines the demand in the}

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are firms that only use past observed excess supply as adjustment mechanism in their pricing strategy; they have a significant coefficient for the lag of the excess supply in model 3. The last

group is the combination of both profit seekers and quantity adjusters and is called adjusters.16

Note that the strategies of firms in the same group may not be exactly the same, as indicated in

observation 7: there might be differences between the strategies used for qi,t and pei,t.

The last 40 periods of each experimental market are simulated; the learning phase is not

simulated. The models that are used to determine pe

i,t , pi,t and qi,t are models 2, 3 and 4

respectively. Hence, the models for the decision variables in the simulations are the same as the estimated models for the experimental outcomes. The coefficients used in the simulations are the estimated ones from tables 6 to 17.

Initial values are the experimental values from periods 9 and 10 for the variables in models 2 to 4. Noise from a N(0, 1/4) distribution is added to the calculation of the decision variables. The number of replications is 10,000. For each group the experimental market is simulated twice: first with firms from that group only and second with all other firms. The second simulation presents a check on the results of the first simulation.

4.2 Simulations results

Tables 4 and 5 show the simulation results for treatment 1 and 2, respectively. As an illustration, figures 4 and 5 graphically show the simulation results for market 2 of treatment 1 ; figures for the other markets can be found in appendix C. The columns for profit seekers and adjusters for market 4 of treatment 1 in table 4 are empty, because none of the firms in that market has a significant coefficient for the profit feedback variable. As a results, the group of profit seekers is empty and the groups of quantity adjusters and adjusters are the same.

The differences between the aggregate outcomes of simulations with a specific group and without that group (the columns indicated with ‘Excluded’) are significant for all but three com-binations as indicated by Mann-Whitney U-tests at p-values smaller than 0.01. The differences between the average prices in period 11 to 30 for simulations with and without quantity adjusters for market 4 of treatment 1 and for market 1 of treatment 2 and for simulations with and without adjusters for market 2 of treatment 1 are the only insignificant ones. However, the differences between those averages in period 31 to 50 of the simulations are significant at p-values smaller

16_{Firms using past observed profits and past observed excess supply are part of the none adjusters group. This}

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Market 2 Market 4

Profit seekers Excluded Profit seekers Excluded

11-30 10.310 8.162 11.274 7.012 - - -

-(0.135) (0.592) (0.215) (0.195) - - -

-31-50 10.365 8.195 11.825 6.801 - - -

-(0.002) (0.010) (0.096) (0.024) - - -

-Quantity adjusters Excluded Quantity adjusters Excluded

11-30 10.206 7.627 12.134 6.742 10.400 7.086 10.483 7.649

(0.315) (0.422) (0.051) (0.106) (0.945) (0.095) (0.246) (0.102)

31-50 10.926 7.121 12.195 6.684 13.190 6.626 10.737 7.618

(0.117) (0.072) (0.003) (0.002) (0.681) (0.681) (0.020) (0.007)

Adjusters None adjusters Adjusters None adjusters

11-30 10.221 7.770 10.304 5.012 - - -

-(0.251) (0.414) (0.486) (0.208) - - -

-31-50 10.728 7.374 10.372 4.796 - - -

-(0.078) (0.071) (0.223) (0.090) - - -

-Table 4: Average simulated prices and quantities for both markets of treatment 1 for rounds 11 to 30 and 31 to 50 (standard deviations in parentheses).

than 0.01. Hence, in the last twenty periods of the experiment, all the differences between the aggregate outcomes of simulations with a specific group and without that group are significant. Observation 8. None adjusters prevent the average market price from reaching the monopolis-tically competitive market equilibrium in most markets. This is clear for market 2 of treatment 1 and market 1 of treatment 2. In market 2 of treatment 1 the simulated market price for none

adjusters is below pM C _{and not converging. Although the average market price in the last twenty}

periods slightly increases from 10.304 to 10.372, this difference is not significant as indicated by a Wilcoxon signed rank test at a p-value of 0.58. In addition, the 95% confidence interval is large and getting wider during the simulation, which confirms that the simulated market price for none

adjusters is not converging towards pM C_{. In market 1 of treatment 2 the average market price in}

the last twenty periods of the simulations with none adjusters only is 5.081, as can be seen from table 5. This is a deviation of more than 50% from the monopolistically competitive market price

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Market 1 Market 2

Profit seekers Excluded Profit seekers Excluded

11-30 10.743 7.364 8.082 6.793 12.734 6.699 11.015 5.999

(0.337) (0.163) (0.111) (0.183) (0.548) (0.258) (0.145) (0.278)

31-50 11.173 7.145 8.369 6.651 13.579 6.296 11.517 5.692

(0.056) (0.035) (0.052) (0.214) (0.091) (0.044) (0.204) (0.031)

Quantity adjusters Excluded Quantity adjusters Excluded

11-30 9.939 7.099 10.050 7.960 8.890 4.777 12.466 7.012

(0.503) (0.148) (0.305) (0.193) (0.123) (0.354) (0.237) (0.057)

31-50 11.438 6.937 10.523 7.644 9.398 4.425 12.699 6.929

(0.316) (0.041) (0.055) (0.038) (0.287) (0.047) (0.007) (0.004)

Adjusters None adjusters Adjusters None adjusters

11-30 10.516 7.138 7.203 4.907 10.271 5.202 12.255 7.249

(0.493) (0.096) (0.882) (0.004) (0.109) (0.289) (0.027) (0.083)

31-50 11.255 7.108 5.081 4.913 10.905 4.834 12.242 7.271

(0.067) (0.011) (0.429) (0.002) (0.255) (0.020) (0.002) (0.002)

Table 5: Average simulated prices and quantities for both markets of treatment 2 for rounds 11 to 30 and 31 to 50 (standard deviations in parentheses).

of 12. Moreover, the average market price in this simulation is diverging from pM C_{, because the}

average market price decreases from 7.203 to 5.081. This difference is significant as indicated by a Wilcoxon signed rank test at a p-value of 0.00. At the same time, the average market prices in the last twenty periods from the simulations with adjusters only in both markets are close to the monopolistically competitive market price. Furthermore, they are also converging towards

pM C_{, because the price in the last twenty periods is significantly closer to p}M C _{as indicated by}

Wilcoxon signed rank tests at p-values of 0.00. This is nicely illustrated by the lower panels of

figures 4 and 7. The simulated market price in the left sub-figure is converging towards pM C and

diverging from pM C in the right sub-figure.

None adjusters also prevent the average market price from converging in the remaining two markets, but for these markets the observation is less clear cut. In market 2 of treatment 2 the

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11 to 50: the simulated market price decreases with only 0.013 ECU from period 11 to 30 to period 31 to 50. Furthermore, with an average value of 12.242 in the last twenty periods, the simulated market price is only slightly different from the monopolistically competitive price of

12. However, the simulated market price for adjusters is converging faster towards pM C as it

increases with 0.634 ECU. This is graphically illustrated in the right sub-figure in the lower panels of figure 9. Hence, it still seems that in this market none adjusters are responsible for keeping the experimental market price above the monopolistically competitive outcome. The simulation results for market 4 of treatment 1 are even less clear-cut. The simulated market price for the group that excludes quantity adjusters (which is equal to none adjusters in this market) stays

below pM C_{with an average of 10.737 in the last twenty periods. However, the simulated price for}

quantity adjusters is also different from the monopolistically competitive price in the last twenty periods and is diverging. Thus, for this market it cannot be said that none adjusters exclusively prevent the average market price from converging.

Observation 9. Extending the information set available to firms with excess demand seems to make profit seekers, next to quantity adjusters, responsible for the converging trend in the average market price. In market 2 of treatment 1 quantity adjusters seem to be responsible for the converging trend. The average simulated market price for this group increases from 10.206 to 10.926 in the last twenty periods. Excluding the quantity adjusters leads to a slightly diverging simulated market price instead of a converging one, although the simulated market price is close

to pM C_{: it increases from 12.134 to 12.195 in the last twenty periods of the experiment. The}

difference between the two prices is significant as indicated by a Wilcoxon signed rank test at a p-value of 0.00. Compared to the quantity adjusters, the profit seekers in this market do exactly the opposite: the simulated market price stays relatively constant in the last twenty periods and

below pM C, as can be seen from the straight green line in the left sub-figure on the top row of

figure 4. This is confirmed by the simulation results excluding the profit seekers: the simulated market price is converging and equal to 11.825 in the last twenty periods, which is very close

to pM C_{. The constant market price below p}M C _{in the simulations for profit seekers might be}

caused by profit seeking firms that have an estimated coefficient for the profit feedback variable that is quite large. If a price increase from those firms leads to a fall in their profits, they might reduce their prices below the monopolistically competitive market price and keep it at that level.

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4 40-periods ahead simulations 24 0 10 20 30 40 50 0 5 10 15 20 25 period price Profit seekers

simulated average price actual average price

0 10 20 30 40 50 0 5 10 15 20 25 period price

Profit seekers (excluded)

0 10 20 30 40 50 0 5 10 15 20 25 period price Quantity adjusters

0 10 20 30 40 50 0 5 10 15 20 25 period price

Quantity adjusters (excluded) simulated average price actual average price

0 10 20 30 40 50 0 5 10 15 20 25 period price Adjusters

0 10 20 30 40 50 0 5 10 15 20 25 period price None adjusters

Figure 4: 50-period ahead simulations for the average market price of treatment 1, market 2; number of replications: 10.000; noise ∼ N(0, 1/4); dotted lines: upper or lower bound of 95% confidence interval. Top row: results for simulations with firm 4, that uses the profit feedback variable, on the left side and without those firms on the right side. Middle row: results for simulations with firms 2, 3, 5 and 8, that use the lag of the excess supply, on the left side and without those firms on the right side. Bottom row: results for simulations with both profit seekers and quantity adjusters (firms 2, 3, 4, 5 and 8) on the left side and without those firms on the right side.

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4 40-periods ahead simulations 25 0 10 20 30 40 50 0 2 4 6 8 10 12 14 16 18 20 period quantity Profit seekers

simulated average quantity actual average quantity

0 10 20 30 40 50 0 2 4 6 8 10 12 14 16 18 20 period quantity

Profit seekers (excluded)

0 10 20 30 40 50 0 2 4 6 8 10 12 14 16 18 20 period quantity Quantity adjusters

0 10 20 30 40 50 0 2 4 6 8 10 12 14 16 18 20 period quantity

Quantity adjusters (excluded) simulated average quantity actual average quantity

0 10 20 30 40 50 0 2 4 6 8 10 12 14 16 18 20 period quantity Adjusters

0 10 20 30 40 50 0 2 4 6 8 10 12 14 16 18 20 period quantity None adjusters

Figure 5: 50-period ahead simulations for the average market quantity of treatment 1, market 2; number of replications: 10.000; noise ∼ N(0, 1/4); dotted lines: upper or lower bound of 95% confidence interval. Top row: results for simulations with firm 4, that uses the profit feedback variable, on the left side and without those firms on the right side. Middle row: results for simulations with firms 2, 3, 5 and 8, that use the lag of the excess supply, on the left side and without those firms on the right side. Bottom row: results for simulations with both profit seekers and quantity adjusters (firms 2, 3, 4, 5 and 8) on the left side and without those firms on the right side.

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The results for market 4 of treatment 1 indicate that the quantity adjusters are responsible for the upward trend in the average market price. However, this does not lead to convergence

as the simulated market price for quantity adjusters crosses pM C _{in period 31. Thereafter, the}

simulated market price is diverging and above pM C. This diverging trend might be due to an

estimated coefficient for the past observed excess supply that is too close to zero for one of the quantity adjusting firms. As a result, that firm might possibly keep increasing its price, because the price decreasing influence of the past observed excess supply is too small. In turn, this could lead to a non-stationary market price and hence, to the diverging trend, as shown in the left sub-figure from the top panels of figure 6.

In treatment 2 profit seekers and quantity adjusters are responsible for the converging trend of the average market price. Recall that the information set is extended with past excess demand in treatment 2, whereas only past observed excess supply is available to firms in treatment 1. The interaction between both groups leads to convergence in market 2. This can easily be seen from the left panels of figure 9. The simulated market price for profit seekers stays above

pM C, for quantity adjusters it stays below pM C, but for the combination of both groups in

the group adjusters, it almost converges. In market 1 of treatment 2 both quantity adjusters and profit seekers are responsible for the converging trend in the average market price. The

simulated market prices for both groups are converging towards pM C _{and the market price in}

the simulations with the combination of both groups is also converging towards pM C_.

Observation 10. Quantity adjusters are responsible for the convergence of the average market quantity towards the monopolistically competitive quantity in most markets. This is as expected, because quantity adjusters are firms that focus on minimizing excess supply (and, in treatment 2, also excess demand), which should lead to average market quantities close to the monopolisti-cally competitive quantity. This is the case for both markets of treatment 1 and market 1 of treatment 2. The simulated market quantity for quantity adjusters in market 2 of treatment 1 decreases from 7.627 to 7.121 in the last twenty periods. This is very close to the monopolisti-cally competitive outcome of 7. Excluding this group from the simulations leads to an average

market quantity that is smaller than and diverging from qM C_{. In market 4 of treatment 1 the}

simulated market quantity for quantity adjusters is also close to qM C _{in the last twenty periods.}

However, it is not as close as it is in periods 11-30. Excluding the quantity adjusters leads to simulated market quantities above the monopolistically competitive equilibrium. Finally, the

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average market quantity in market 1 of treatment 2 converges almost immediately towards qM C_,

while excluding this group leads to simulated market quantities above qM C_{. Figures 5, 6 and 8}

illustrate this observation graphically.

Interestingly, quantity adjusters seem to have the opposite effect in market 2 of treatment 2. The average market quantity is 4.425 in the final twenty periods of the simulations for quantity adjusters. In this market the combination of profit seekers and none adjusters is responsible for the convergence of the average market quantity. This is the case because the average market

quantity is slightly above or below qM C _{in the simulations with either profit seekers or none}

adjusters, while it is 6.929 in the simulation with both groups and hence, almost equal to qM C_.17

Summarizing the above, the average market prices in the experimental markets do not fully converge towards the monopolistically competitive market price due to the heterogeneity in the strategies of the firms. None adjusters are responsible for this non-convergence in most markets. Quantity adjusters are responsible for the converging trend, while extending the information set makes quantity adjusters and profit seekers responsible. The convergence of the average market quantities in most of the experimental markets is due to the quantity adjusters.

The results from the simulations have some limitations. Most importantly, the groups used in the simulations are not homogeneous with respect to their strategies for all three decision variables. As explained in section 4.1, the division of the firms into the three groups is based on their price setting strategy, but firms with the same price setting strategy do differ in their forecasting and quantity setting strategies. This might influence the results, because the forecast of the average market price is used as input in both the price and quantity setting strategy and the price firms set is used as input in the quantity setting strategy.

Furthermore, the coefficients for the significant variables may differ for firms in the same group, which may lead to firms with the same strategy ending up at different price and quantity levels. In addition, firms in the same group might also have different significant variables, next to the one that defines the group. For example, quantity adjusting firms always have the past ob-served excess supply significant in their pricing strategy, but past forecasts of the average market price might or might not be significant. However, next to these drawbacks, using the estimated strategies in the simulations has the advantage that the actual impact of those strategies on the experimental market outcomes can be assessed.

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5 Conclusion 28

Finally, simulations with isolated groups do not capture the interaction between different groups. In the experiment, firms also base their decisions on the actions of others, for example on the average market price. However, the average market price in a simulation with one group only is different from the experimental market price. Hence, the actions of the firms in that group might be different in the experiment and the simulations. However, part of this interaction is already captured, because each experimental market is simulated twice for each group: with and

without that group. The simulation without a specific group includes the remaining groups18

and hence partly captures the interaction in the market.

5 Conclusion

This thesis has investigated whether monopolistically competitive market outcomes are reached in experimental markets, and if so, how. It did so by analyzing part of the outcomes of a laboratory experiment, conducted by Assenza et al. (2013a), in which human subjects acted as firms in a monopolistically competitive market environment. The experiment has two important novel features. First of all, firms have limited information about the market environment and second, they have to set production in advance.

The main conclusion that can be drawn from the analysis in this thesis is that aggregate market outcomes converge towards monopolistically competitive outcomes, but do not always reach them, due to the heterogeneity in the price and quantity setting strategies of individual firms. In order to reach this conclusion, the experimental outcomes have been analyzed and models for the individual strategies of the firms have been estimated. Moreover, 40-periods ahead simulations have been conducted to understand the impact of the different strategies employed by the firms on the aggregate outcomes of the experimental markets. In these simulations, firms are grouped by their pricing strategy and the estimated models for the firms are used to determine the decision variables.

The experimental results show that the average market prices converge towards, but stay slightly above or below the monopolistically competitive price. Average market quantities con-verge towards monopolistically competitive levels in the first rounds of each experimental market. On the level of the individual firm, prices are converging towards the monopolistically competitive

18_{For the simulations of the adjusters this is the opposite: the group adjusters includes two groups, quantity}

Price and quantity setting in monopolistic competition.

Faculty of Economics and Business

Master thesis