# Contributions to applied welfare analysis : Introducing novel methods for exact welfare analysis based on differential demand functions

##### Pöyry, Matias (2022)

Pöyry, Matias

2022

Kauppatieteiden maisteriohjelma - Master's Programme in Business Studies

Johtamisen ja talouden tiedekunta - Faculty of Management and Business

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##### Hyväksymispäivämäärä

2022-12-08**Julkaisun pysyvä osoite on**

https://urn.fi/URN:NBN:fi:tuni-202212088970

##### Tiivistelmä

In this thesis I study applied welfare analysis as well as contribute to the methodology. In particular, I focus on how theoretically exact welfare analysis can be based on demand systems and functions. This has practical significance since demand functions are observable in principle, as opposed to expenditure and utility functions on which theoretically exact welfare analysis is often based. It’s a common misconception that theoretically exact welfare analysis necessitates knowledge of some unobservable construct. However, it’s been shown that one only needs to assume that the demand functions are known so there’s no need to make further assumptions.

The main contribution of this thesis are novel methods for numerical welfare analysis, which allows one to estimate the welfare effects of price changes based on differential demand functions. This sets the algorithms apart from other proposed methods which rely on demand functions specified in levels. This is of importance since economic time series are often non-stationary, which if ignored can lead to severe econometric problems when estimating demand functions. Non-stationary series can often be made stationary by differencing. With differenced data it is natural to use differential demand functions, so the novel algorithms are a valuable asset in welfare analysis based on time-series.

Welfare analysis is not concerned with just price changes, and one interesting object of study is rationing. In rational consumer theory, the consumer is expected to choose her preferred bundle within the limitations set by market prices and her budget. Rationing may lead to welfare losses if the consumer must choose a less preferred bundle than she would choose when only limited by the prices and budget. Central to the theory of rationing are virtual prices, which would induce an unconstrained consumer to choose the rationed bundle. The theory of rationing allows us to shift the focus of the analysis from quantity changes to virtual price changes, the welfare effects of which can be estimated with the novel algorithms. The virtual price approach to welfare analysis is generally not well known, and in this thesis, I aim to make the subject more approachable by providing some insights to the matter along with a few novel results.

Rationing is an ever-present, yet often neglected, phenomenon in modern economies. Recently, the COVID-19 pandemic has piqued public interest in rationing as there have been sudden constraints on consumption. To illustrate some of the potential of the novel methods, I estimate the welfare effects of rationing related to COVID-19 in Finland during the year 2020. To estimate the virtual prices changes and their welfare effects, I estimate four well-known differential demand systems at the aggregate level in Finland. In addition, I estimate log-linear demand functions in differenced form at a less aggregated level. The data used consists of household expenditure from the System of National Accounts, consumer price index and population structure data spanning from 1975 to 2020, which is provided by Statistics Finland. I estimated the differential demand systems with the iterated Seemingly Unrelated Regression method, which accounts for contemporaneous correlation of the error terms. I estimated the log-linear differential demand functions with Four-Stage Aitken method, which also accounts for autocorrelation of the error terms. The welfare effects of the virtual price changes were estimated by Hausman’s method, local approximations, and the novel numerical methods.

According to the estimates based on the aggregate models, the welfare losses due to rationing were approximately 400–500 million euros in 2020. During that year, the final expenditure of households fell drastically by 4 133 million euros, so the welfare effects of rationing correspond roughly to 10–12% of the severity of the income shock. However, the welfare analysis at the less aggregated level resulted in greater estimates, indicating that the aggregate models may suffer from aggregation bias and the magnitudes of these welfare estimates are likely biased downwards. Furthermore, the estimated demand systems didn’t satisfy the integrability conditions, so the results are best viewed as approximations. The novel methods were demonstrated to work well in practice and were found to converge towards the true values.

The main contribution of this thesis are novel methods for numerical welfare analysis, which allows one to estimate the welfare effects of price changes based on differential demand functions. This sets the algorithms apart from other proposed methods which rely on demand functions specified in levels. This is of importance since economic time series are often non-stationary, which if ignored can lead to severe econometric problems when estimating demand functions. Non-stationary series can often be made stationary by differencing. With differenced data it is natural to use differential demand functions, so the novel algorithms are a valuable asset in welfare analysis based on time-series.

Welfare analysis is not concerned with just price changes, and one interesting object of study is rationing. In rational consumer theory, the consumer is expected to choose her preferred bundle within the limitations set by market prices and her budget. Rationing may lead to welfare losses if the consumer must choose a less preferred bundle than she would choose when only limited by the prices and budget. Central to the theory of rationing are virtual prices, which would induce an unconstrained consumer to choose the rationed bundle. The theory of rationing allows us to shift the focus of the analysis from quantity changes to virtual price changes, the welfare effects of which can be estimated with the novel algorithms. The virtual price approach to welfare analysis is generally not well known, and in this thesis, I aim to make the subject more approachable by providing some insights to the matter along with a few novel results.

Rationing is an ever-present, yet often neglected, phenomenon in modern economies. Recently, the COVID-19 pandemic has piqued public interest in rationing as there have been sudden constraints on consumption. To illustrate some of the potential of the novel methods, I estimate the welfare effects of rationing related to COVID-19 in Finland during the year 2020. To estimate the virtual prices changes and their welfare effects, I estimate four well-known differential demand systems at the aggregate level in Finland. In addition, I estimate log-linear demand functions in differenced form at a less aggregated level. The data used consists of household expenditure from the System of National Accounts, consumer price index and population structure data spanning from 1975 to 2020, which is provided by Statistics Finland. I estimated the differential demand systems with the iterated Seemingly Unrelated Regression method, which accounts for contemporaneous correlation of the error terms. I estimated the log-linear differential demand functions with Four-Stage Aitken method, which also accounts for autocorrelation of the error terms. The welfare effects of the virtual price changes were estimated by Hausman’s method, local approximations, and the novel numerical methods.

According to the estimates based on the aggregate models, the welfare losses due to rationing were approximately 400–500 million euros in 2020. During that year, the final expenditure of households fell drastically by 4 133 million euros, so the welfare effects of rationing correspond roughly to 10–12% of the severity of the income shock. However, the welfare analysis at the less aggregated level resulted in greater estimates, indicating that the aggregate models may suffer from aggregation bias and the magnitudes of these welfare estimates are likely biased downwards. Furthermore, the estimated demand systems didn’t satisfy the integrability conditions, so the results are best viewed as approximations. The novel methods were demonstrated to work well in practice and were found to converge towards the true values.