## Research & Publications

## Publications

'Equilibrium Pricing under Concave Advertising Costs'

The B.E. Journal of Theoretical Economics, 2022. (With Klaus Kultti)

Abstract

We study Butters’s (1977. “Equilibrium Distributions of Sales and Advertising Prices.” The Review of Economic Studies 44 (3): 465–91) model under concave advertising costs, and determine a class of cost functions such that each seller sends the same finite number of ads in equilibrium. Then we consider the limit economy where the number of buyers and sellers grow indefinitely, and show that the equilibrium of the finite economy does not converge to an equilibrium in the limit economy.

'Equilibrium Price and Advertisement Distributions'

Journal of Mathematical Economics, 97: 102535, 2021. (With Klaus Kultti)

Abstract

We consider an economy where many sellers sell identical goods to many buyers. Each seller has a unit supply and each buyer has a unit demand. The only possible information flow about prices is through costly advertising. We show that in equilibrium the sellers use mixed strategies in pricing which leads to price and advertisement distributions. With convex advertising costs each seller sends only one advertisement in the market. We also delineate a class of advertising costs which ensures that sellers may send multiple advertisements in equilibrium. Higher prices are advertised more than lower prices.

## Working Papers

We consider a principal-agent model in which the principal can monitor and punish the agent with a fine if the agent is caught being untruthful. To reduce the probability of being verified, the agent can engage in costly avoidance. We design the optimal regulatory policies with and without avoidance. The optimal mechanism with enforcement allocates the object more often than the optimal mechanism without enforcement. Moreover, enforcement increases the expected transfers to the principal. Avoidance has two implications to the optimal regulatory mechanism: (i) the expected optimal transfers to the principal decrease and (ii) the principal allocates the object to a smaller share of types. If the latter effect dominates the former, it is possible that the agent's capability to engage in avoidance is disadvantageous not only for the principal, but also for the agent ex ante.

We study a market for 'lemons' from the perspective of mechanism design in a bilateral trade setup. The closed-form solution for the seller-optimal safe mechanism under one-sided private information is provided. We show that a seller can disclose the quality of the goods by controlling the supply of her goods; high-quality sellers want their goods to be scarce and expensive and low-quality sellers abundant and cheap. In this way, sellers can differentiate their products from each other and maximize their payoffs. We extend this model to two-sided private information and give a novel characterization of the seller-optimal safe mechanism in this setup. It turns out that if there is two-sided asymmetric information, then the seller finds it optimal to engage in price signalling instead of quantity signaling. This is the least-cost way for the seller to signal her private information to the buyer.

'Mechanism Design with Auditing and Avoidance: Tax Evasion Story'

SSRN: 4230382, 2022. (With Petteri Palonen)

Abstract

We consider a principal-agent model where the agent is a taxpayer and the principal is a tax authority. The principal wants to know the agent’s income so that she can then assign an appropriate tax to the agent. The tax authority can investigate whether the taxpayer's income report was in fact truthful. If the taxpayer is caught for misreporting, he is punished by a fine. We assume that the taxpayer can engage in avoidance activities that undermine the tax authority's audit efforts, and thus, reduce the probability of being caught for lying. We find that in addition to information rent, it is optimal for the tax authority to give the taxpayer 'avoidance rent'; because the agent can decrease the probability of being caught for misreporting, it is optimal for the principal to audit less intensively and give some additional rent to the agent instead.

We study the price competition between two firms that have to advertise to reach consumers. Advertising can be either informative or persuasive (branding); the latter increases consumers' willingness to pay. When both firms advertise informatively, the pricing is in mixed strategies, and the profits are non-monotone in advertising costs. When the firms engage in different advertising methods, the pricing is in pure strategies, and the firm with persuasive advertising may choose a price that is higher than the monopoly price.

We consider a finite economy with men and women. The agents have status concerns such that when a particular agent has k agents of the same type below him/her in the income distribution, he/she gets utility kA, where A>0, from status. Acquiring income is costly and once the income distribution is realised, the men and women form pairs in a positive assortative manner. A pair shares its income and the gains from status are realised only after the pairs are formed. The income acquisition game has the equilibrium in mixed strategies, and the prize distribution, i.e. partner's income and attainable status, is an equilibrium object. We show that contrary to the case where the prize distribution is exogenous not all the gains are competed away. This is because income sharing leads to free riding which mitigates the wasteful competition for status. We also show that the heterogeneity of the agents has the same effect even if the the prize distribution is exogenous.

'When Aiyagari meets Piketty: Growth, Inequality and Factor Income Shares'

SSRN: 3782991, 2022. (With Toni Juuti, Kari Heimonen, and Juha-Pekka Junttila)

Abstract

This study reveals that the relationship between economic growth and income inequality is conditional on functional income distribution and financial development. Using historical data, we demonstrate that when the capital share of income is low, a positive relationship is discernible between top income shares and growth in GDP per capita; meanwhile, this relationship becomes negative when the capital share is high. These results hold only under modest financial frictions. Under more stringent financial conditions, the relationship between inequality and growth becomes positive and increases in strength as capital share increases. We show that these empirical patterns are compatible with an Aiyagari-type theoretical model that emphasises how changes in the distribution of income translate into the accumulation of physical capital and overall economic activity through precautionary saving motives and consumption smoothing.

## Work in Progress

We derive the optimal auction design with costly verification. In the symmetric setup, the optimal mechanism can be implemented by the second-price auction with a reserve price and an additional payment for the winner. This extra payment can be interpreted as a royalty payment which is not based only on the winner's bid but also on the second-highest bid. The royalty payment is determined by the auctioneer's ability to verify the winner's private information and marginal punishments. Compared with the optimal Myerson auction (1981), we find that in the optimal auction with verification, the optimal reserve price is lower and the auctioneer's surplus greater. In some instances, it is optimal for the auctioneer to allocate the object to several buyers, which can be interpreted as a joint project or joint ownership of the minerals.

'Identification of Collusion from Entry Decisions'

2022. (With Riku Buri, Carlo Perroni, and Janne Tukiainen)

Abstract

We study how to detect collusion from observed entry choices. We build a model of a repeated entry game in which there are two firms facing identical production technologies, symmetric demand conditions, and heterogeneous entry costs drawn from identical distributions. The firms can collude under indefinite repetition. We provide identification methods for collusion under complete and incomplete information.

'Allocation Equivalence Theorem'

2022.

Abstract

The revenue equivalence theorem by Myerson (1981) states that the equilibrium transfers in a canonical auction model are pinned down by the equilibrium allocation rule and a constant term. I derive the converse of this relation, namely, the allocation equivalence theorem, which states that the equilibrium allocation rule is pinned down by the equilibrium transfer rule and a constant. This theorem is applicable, for example, to verification models and, particularly, to mechanism design without transfers where the principal can use verification and punishments to incentivize the agent. In this case, the allocation rule is determined by exogenously given verification and punishments functions.

## Other Publications and Policy Related Work

'The Finnish gambling system in transition – Options for the future'

Publications of the Finnish Government 2021:12, 2021. (With Erkki Liikanen, Liisa Hyssälä, Kalevi Kivistö, Osmo Soininvaara, and Ulla-Maj Wideroos)

Abstract

Gambling-related harm is perceived as being of major consequence for the wellbeing of society, which is why it has been considered necessary to intervene by legislative means and to step up the actions to promote responsible gambling. Additionally, slot machines have been kept closed due to the coronavirus epidemic. Veikkaus Oy estimates that, as a result of the actions taken, the gambling revenue annually remitted to the state will be reduced by about EUR 300 million. While the gambling-related harm is reduced, this means that the funding of the beneficiaries financed with gambling revenue will be reduced as well.

This report examines four different options for the development of the Finnish gambling system. The working group sets as its primary option an overall reform that allocates gambling revenue to general state income and transfers the current beneficiaries under the budgetary framework procedure. Careful preparation and a plan are needed for sizing, enhancing and assessing the effectiveness of the funding awarded for the beneficiaries and the activities of non-governmental organisations. The stability of the funding could be increased if the order of magnitude of the funding could be determined for a period longer than just one electoral term. The working group estimates that the reform could be implemented starting from the beginning of 2024.

'Big Data and Machine Learning in Macroeconomics'

Finnish Economic Journal, 2018 (2). (In Finnish)

Abstract

Economists have started to use large datasets, or so-called big data, in their research. There has been a tremendous increase in the number of different statistical sources and statistical forms, which has required new working methods also from the statistical and computer sciences side. This review examines the use of big data in macroeconomics research and forecasting. The article also introduces a few methods of machine learning for processing and analyzing large datasets. The key objective of the review is to take a broad look at what new ever-growing data and machine learning have brought to macroeconomics.

'The Structural Changes in Finnish Industrial Sector'

Bank of Finland Bulletin, 2017 (11). (In Finnish)

Abstract

Finland's industrial sector has waned in many respects between 2000 and 2014. Imported products are more used in industrial production, and the employment impact of industry has decreased significantly. However, through intermediate inputs, industry remains strongly linked to the growing service sector. A review of industry and service structures gives clear signs that the service sector is going to grow further. But this does not render the role of industry irrelevant.

I study the lower bounds on nominal interest rates by constructing models for an agent's portfolio optimisation problem of risk-free assets. The question “is there a lower bound on nominal interest rates, and is it zero” is approached theoretically by considering the situation where a depositor decides whether to keep her money in a bank account or turn the deposits into cash or some other cash-equivalent. The two-period and multi-period models presented in this paper are applicable for examining the lower bounds on commercial bank deposit rates and central bank policy rates. The multi-period model with a stochastic cash holding cost function provides a novel framework and tool for the yields of risk-free assets. By using this model, it is possible to simulate asset returns and thereby approach the lower bounds on deposit rates. The results indicate that the lower bound on nominal interest rates is negative.