One of the hot areas for econometric research in recent years has been spatial econometrics. Think of it, at least initially as time series econometrics in a different dimension. One interesting aspect of it is that instead of being single-dimensional like time series, it can be two-dimensional, or even more I guess. This field brings interesting new challenges, and it must be exciting working in this field. However, as too often in econometric theory, research becomes quickly detached from reality, and more specifically from the needs of empiricists. N never goes to infinity, for example.
Luisa Corrado and Bernard Fingleton bring forward another important point. These techniques are used to test economic theories, so one should be able to embed some restrictions from economic theory. It is all nice and sweet when one can find an optimal weighting matrix with the right properties, but it is useless if the found weights cannot be matched with anything one wants to test. The causality goes the wrong way: first determine restrictions from the theory, then use the constraints to find the optimal weighting matrix.
This is not just a theoretical consideration. Spatial lags are crucial in spatial econometrics and are suppose to capture some network effects. But they can also soak up the impact of latent or unobserved variables, as in "regular" econometrics. This can lead to severe miss-specification and biased inference, somethings one is all to familiar with using lags in time series. In fact, one should be downright suspicious of any time-series results that only holds when lagged dependent variables are used. The same must apply to spatial econometrics.
Showing posts with label measurement. Show all posts
Showing posts with label measurement. Show all posts
Risk preferences are heterogeneous across countries
In any international economic model I can think of, or any study comparing countries using economic models with utility maximizing utility, it is never considered that the preferences of households may differ. In closed economy models, some heterogeneity in preferences may be considered, but it is generally avoided because it is difficult to measure and in most cases would not make much a different anyway. But if we are thinking about some international imbalances, why not think about differences in aggregate preferences?
Marc Oliver Rieger, Mei Wang and Thorsten Hens look at the results of a survey administered across 45 countries that tries to elicit measurements about risk aversion, loss aversion and subjective probabilities. Too bad they did not consider discounting and the intertemporal elasticity of substitution. Anyway, they find that there are actually large differences across countries, differences that they attribute partially to economic conditions and "culture." For the former, the authors looks a GDP per capita and the human development index. I would also have looked at a measure of financial development. It seems to me that people become financially more sophisticated and thus willing to take risks if they are more exposed to financial markets. But I can be proven wrong.
Marc Oliver Rieger, Mei Wang and Thorsten Hens look at the results of a survey administered across 45 countries that tries to elicit measurements about risk aversion, loss aversion and subjective probabilities. Too bad they did not consider discounting and the intertemporal elasticity of substitution. Anyway, they find that there are actually large differences across countries, differences that they attribute partially to economic conditions and "culture." For the former, the authors looks a GDP per capita and the human development index. I would also have looked at a measure of financial development. It seems to me that people become financially more sophisticated and thus willing to take risks if they are more exposed to financial markets. But I can be proven wrong.
A history of national accounting
We use national account data without realizing the efforts that lie behind the construction of these account. And frankly, it is sometimes like sausage making, but less and less so as the United Nations have managed to enforce rather widely its standards. But getting to these standards has been a very process.
Frits Bos documents the history of national accounting over three centuries. He shows that significant efforts and advances in national accounting arouse from two kinds of needs: understanding recent major crises and the increase of influence of the state and its policy making. To fix an economy, you need to know what is wrong with it, or at least the symptoms. To set policy, one needs measures to establish goals and how they have been reached.
Frits Bos documents the history of national accounting over three centuries. He shows that significant efforts and advances in national accounting arouse from two kinds of needs: understanding recent major crises and the increase of influence of the state and its policy making. To fix an economy, you need to know what is wrong with it, or at least the symptoms. To set policy, one needs measures to establish goals and how they have been reached.
How much tax evasion is there in the US?
As mentioned before, tax authorities are now especially eager to catch tax evaders. But how many of those are actually out there? One would suspect that there are relatively few of them in a low tax country like the United States. But again, the tax authority there has been given relatively few means to pursue investigations and audit rates are surprisingly low. And the tax code is so complicated that the line between tax evasion and confusion is rather blurred.
The Internal Revenue Service, the US federal tax authority, has estimates about how much it is missing in revenue, but as far as I know these numbers are kept well hidden, except for a study in the eighties. Academics have tried to replicate this exercise, obviously with poorer data than the IRS, but with less political pressure. The latest attempt is by Edgar Feige and Richard Cebula. They use a technique similar to one used to calculate the size of an informal economy, a technique based on the quantity of currency in circulation and of check deposits, adjusting for currency suspected abroad and financial innovation. Indeed, tax evaders try to hide income from reporting by using cash transactions. This ignores though those who use tax havens, and I welcome informed guesses on how large a factor that may be.
In any case, Feige and Cebula come to the conclusion that about 20% of reportable income is not properly reported, leading to lost revenue in the order of $400-500 billion every year. They even compute a time series that allows them to figure out what makes the non-compliance rate change. It will not surprise that it increases when national income is higher, when tax rates are higher or when nominal interest rates are higher. It is interesting to see that higher unemployment rates lead to higher non-compliance. That may have to do with more people getting informal income while on unemployment insurance. Still, I cannot shake the feeling that all these results are shaky themselves, as this data is essentially made up.
The Internal Revenue Service, the US federal tax authority, has estimates about how much it is missing in revenue, but as far as I know these numbers are kept well hidden, except for a study in the eighties. Academics have tried to replicate this exercise, obviously with poorer data than the IRS, but with less political pressure. The latest attempt is by Edgar Feige and Richard Cebula. They use a technique similar to one used to calculate the size of an informal economy, a technique based on the quantity of currency in circulation and of check deposits, adjusting for currency suspected abroad and financial innovation. Indeed, tax evaders try to hide income from reporting by using cash transactions. This ignores though those who use tax havens, and I welcome informed guesses on how large a factor that may be.
In any case, Feige and Cebula come to the conclusion that about 20% of reportable income is not properly reported, leading to lost revenue in the order of $400-500 billion every year. They even compute a time series that allows them to figure out what makes the non-compliance rate change. It will not surprise that it increases when national income is higher, when tax rates are higher or when nominal interest rates are higher. It is interesting to see that higher unemployment rates lead to higher non-compliance. That may have to do with more people getting informal income while on unemployment insurance. Still, I cannot shake the feeling that all these results are shaky themselves, as this data is essentially made up.
Better GDP estimates
GDP equals C+I+G+X-M. It also equals national income, at least in theory. But estimates differs widely, even for the United States, which is rather disturbing. How do you conduct proper economic policy when estimates of GDP, even after revisions can differ by more than 2% points and their growth rates have a correlation coefficients of only 0.63 (see the work of Jeremy Nalewaik)?
Boragan Aruoba, Francis Diebold, Jeremy Nalewaik, Frank Schorfheide and Dongho Song make the old diversification of risk argument: why not combine both estimates? After all, this is often done with forecasts, and the two estimates can be treated like forecasts of the true GDP. And consistently with this literature, the weights on each should depend on the variance of the errors. Of course, they are not observed, but the authors have some guesstimates, based on correlations with variables not used to construct either GDP measure that are supposed to be correlated with the true GDP. They then show that measurement matters, for example in dating business cycles. We'll see whether the US will adopt such averaging, as some other countries already do.
Addendum: I wonder how the recent major revisions to US GDP would have fared with this scheme.
Boragan Aruoba, Francis Diebold, Jeremy Nalewaik, Frank Schorfheide and Dongho Song make the old diversification of risk argument: why not combine both estimates? After all, this is often done with forecasts, and the two estimates can be treated like forecasts of the true GDP. And consistently with this literature, the weights on each should depend on the variance of the errors. Of course, they are not observed, but the authors have some guesstimates, based on correlations with variables not used to construct either GDP measure that are supposed to be correlated with the true GDP. They then show that measurement matters, for example in dating business cycles. We'll see whether the US will adopt such averaging, as some other countries already do.
Addendum: I wonder how the recent major revisions to US GDP would have fared with this scheme.
Is it cheaper to live in poor economies?
If you are a rich country resident and travel to a poor country, you are continuously amazed how inexpensive life is there. One rationalizes this with the lower local wages which make domestic goods (and price discriminating imports) cheaper. Is this anecdotal evidence true in general? Does it hold across all countries?
Fadi Hassan finds that indeed rich countries have higher price levels. But once you go further down the development ladder, the statistical evidence is not that clear, and once you reach the lowest rungs, the cost of things could be increasing again. This analysis is performed using the ratio of purchasing power parity to the exchange rate, as measured in the Penn World Tables and finds that the best non-linear fit of the price-income relationship is not increasing for 40% of the countries. The challenge is now to understand why it is so.
Fadi Hassan finds that indeed rich countries have higher price levels. But once you go further down the development ladder, the statistical evidence is not that clear, and once you reach the lowest rungs, the cost of things could be increasing again. This analysis is performed using the ratio of purchasing power parity to the exchange rate, as measured in the Penn World Tables and finds that the best non-linear fit of the price-income relationship is not increasing for 40% of the countries. The challenge is now to understand why it is so.
Do not waste degrees of freedom with macro data
Dealing with microdata is relatively easy, as you have plenty of data points and can freely add explanatory variables with running the risk of running out of degrees of freedom. The story is different for macrodata, as series are much shorter, and one can quickly eat degrees of freedom by using lagged variables. The prime example here are the often abused vector autoregressions (VAR), that get larger and larger, and faster than new data points accumulate. The latest fad is to run regressions with time varying parameters, including in VARs, which is deadly for degrees of freedom as this is roughly equivalent to adding a boatload of dummy variables to the mix. Hence the need to be more parsimonious.
How parsimonious should one be? Joshua Chan, Gary Koop, Roberto Leon-Gonzalez and Rodney Strachan think the solution is in time-varying parsimony. The idea is that sometimes one needs a more complex model, and sometimes a few variables are sufficient. While this allows to spare degrees of freedom when one can do with few variables, this gain on paper is lost, and probably more than lost, by the implicit degrees of freedom used in selecting the right model. This is an old problem than is swept under the rug is many empirical applications, but in this case it becomes even more apparent because so many parameters and models are involved.
How parsimonious should one be? Joshua Chan, Gary Koop, Roberto Leon-Gonzalez and Rodney Strachan think the solution is in time-varying parsimony. The idea is that sometimes one needs a more complex model, and sometimes a few variables are sufficient. While this allows to spare degrees of freedom when one can do with few variables, this gain on paper is lost, and probably more than lost, by the implicit degrees of freedom used in selecting the right model. This is an old problem than is swept under the rug is many empirical applications, but in this case it becomes even more apparent because so many parameters and models are involved.
On the decline of the US manufacturing wage
It is always interesting to see how real wages evolve, as they allow to understand how much a worker can buy from his income. Usually, this is done by dividing the nominal wage by a price index, usually the commodities said worker would typically buy. The results may vary considerably, as a different price index is needed for different workers, and the basket of goods may also vary over time. The latter is particularly important when the sample period is long. It also depends whether you look a hourly, weekly or annual income, and how benefits are included.
John Pencavel reviews a centuries old literature on the topic that came to the conclusion that except for some periods on stagnation, real wages generally were upward bound. He then comes up with his own indexing procedure, and finds that real wages in the US manufacturing sector have declined by 40% since 1960. Wow, this seems to be a real big result, and this requires understanding how this was computed. Indeed, Pencavel does not measure the real wage in the conventional way, but rather the ratio of what workers get to what they could get if the firm made no profit. This does not necessarily mean that the buying power of the worker has decreased by 40%. but rather that a smaller share of firm income goes to labor. With the increased mechanization of manufacturing, this evolution should not surprise many people. But this is not necessarily a 40% fall in real wages as advertised in the paper's abstract.
John Pencavel reviews a centuries old literature on the topic that came to the conclusion that except for some periods on stagnation, real wages generally were upward bound. He then comes up with his own indexing procedure, and finds that real wages in the US manufacturing sector have declined by 40% since 1960. Wow, this seems to be a real big result, and this requires understanding how this was computed. Indeed, Pencavel does not measure the real wage in the conventional way, but rather the ratio of what workers get to what they could get if the firm made no profit. This does not necessarily mean that the buying power of the worker has decreased by 40%. but rather that a smaller share of firm income goes to labor. With the increased mechanization of manufacturing, this evolution should not surprise many people. But this is not necessarily a 40% fall in real wages as advertised in the paper's abstract.
Seasonal adjustment is difficult
As undergraduates, we are taught to make sure the macroeconomic data we are dealing with is seasonally adjusted. We are explained that statistical offices remove the seasonal factors is a way that is close to regressing the data on seasonal dummies and taking moving averages. If you really look into this, as so often, it turns out things are much more complex than that, and subtleties matter.
Stephen Pollock and Emi Mise do a technical review of the various methods and look at some alternatives. Broadly speaking, there are three strands of techniques. The first is based on ARIMA, the second removes seasonal frequencies found in a periodogram, and the third relies on clear distinctions between fundamental and seasonal components in spectral analysis. The difficulties are compounded by the fact that data usually has a trend, which may not be loglinear, and data thus requires pre- and post-treating. And as Pollock and Mise show, each of these methods matter, even for dating turning points. I can imagine this can become even more important when one throws data into a regression, especially if the series have been detrended in different ways. And it is rare to see statistical offices declare what method was used for that.
Stephen Pollock and Emi Mise do a technical review of the various methods and look at some alternatives. Broadly speaking, there are three strands of techniques. The first is based on ARIMA, the second removes seasonal frequencies found in a periodogram, and the third relies on clear distinctions between fundamental and seasonal components in spectral analysis. The difficulties are compounded by the fact that data usually has a trend, which may not be loglinear, and data thus requires pre- and post-treating. And as Pollock and Mise show, each of these methods matter, even for dating turning points. I can imagine this can become even more important when one throws data into a regression, especially if the series have been detrended in different ways. And it is rare to see statistical offices declare what method was used for that.
Price points, good diversity and price rigidity
Much of the real impact of monetary policy hinges on some sort of rigidity in some prices. As regular readers must have noticed, I am not convinced I am not convinced that prices a rigid to the point that it matters, and I am particularly appalled how price rigidity is introduced in theoretical models. Let us have a look at some of latest research on price rigidity.
Edward Knottek uses supermarket scanner to find that price points are much more important than menu costs in determining prices. Price points are for example prices ending in 9, which make up 60% of retail prices. He also finds that in all but 10% of cases, prices return to the previous level after a sale. These two facts cannot be reconciled with menu costs being of relevance. Yet menu costs are the foundation, explicitly or implicitly of almost all models of price rigidity.
Saroj Bhattarai and Raphael Schoenle use producer prices and establish interesting patterns in decisions to change prices. They find that firms with a large variety of goods change prices more frequently, but by smaller amounts. If they change a price, they are more likely to decrease it, and the variance of positive price changes is larger. They also find that for a model to replicate such facts, one needs firm-specific menu costs and state-dependent pricing. This is definitely not Calvo pricing.
Edward Knottek uses supermarket scanner to find that price points are much more important than menu costs in determining prices. Price points are for example prices ending in 9, which make up 60% of retail prices. He also finds that in all but 10% of cases, prices return to the previous level after a sale. These two facts cannot be reconciled with menu costs being of relevance. Yet menu costs are the foundation, explicitly or implicitly of almost all models of price rigidity.
Saroj Bhattarai and Raphael Schoenle use producer prices and establish interesting patterns in decisions to change prices. They find that firms with a large variety of goods change prices more frequently, but by smaller amounts. If they change a price, they are more likely to decrease it, and the variance of positive price changes is larger. They also find that for a model to replicate such facts, one needs firm-specific menu costs and state-dependent pricing. This is definitely not Calvo pricing.
How to measure governance
There is now a cottage industry trying to measure how well countries are governed, in particular how bad corruption is, or how well the rule of law is imposed. These indicators are important, they can determine where foreign direct investment is taking place, whether development aid is disbursed, or whether policy reform has been successful. Thus, it is critical that governance be well measured.
Charles Oman and Christiane Arndt point out that most measures are based on perceptions, which are notoriously biased and difficult to change in the face of hard facts. But their is also substantial danger in that users tend to misread these indicators. For one, they are not precise and should only be interpreted as giving a rough picture. Even when intervals of error are provided, they are often ignored by users. Second, international comparison is difficult because the sources used to construct the index differ widely from one country to the next. Third, a single index is used for many different purposes, and each of those purposes should weigh differently the components of the index. Finally, there is no theory that tells us how to scale the measured before or during the determination of a governance index. And let us not forget most measures are subjective, as they are based on opinions. It frightens me when such an index is used in a regression, especially without any robustness test.
Charles Oman and Christiane Arndt point out that most measures are based on perceptions, which are notoriously biased and difficult to change in the face of hard facts. But their is also substantial danger in that users tend to misread these indicators. For one, they are not precise and should only be interpreted as giving a rough picture. Even when intervals of error are provided, they are often ignored by users. Second, international comparison is difficult because the sources used to construct the index differ widely from one country to the next. Third, a single index is used for many different purposes, and each of those purposes should weigh differently the components of the index. Finally, there is no theory that tells us how to scale the measured before or during the determination of a governance index. And let us not forget most measures are subjective, as they are based on opinions. It frightens me when such an index is used in a regression, especially without any robustness test.
Maximizing the Human Development Index
We all recognize GDP per capita is far from a perfect measure of wellbeing in an economy, hence the Human Development Index (HDI) was developed. It aggregates indicators of health, education and income. The idea is to evaluate how well an individual can function in such an economy. But the elaboration of the HDI did not follow any formal theory in the selection of the precise indicators and their weighting. So what about doing the reverse: take the HDI seriously in theory?
Merwan Engineer and Ian King use a standard growth model, calibrated following Mankiw, Romer and Weil, and look for what it takes to maximize the HDI. And they find massive overinvestment into physical and human capital, which saving rates so much higher than what the Golden Rule would call for that consumption is almost reduced to zero. Because consumption is not part of HDI! That looks a crass oversight, as we generally assume, correctly I think, that people care about consumption for their standard of living.
Merwan Engineer and Ian King use a standard growth model, calibrated following Mankiw, Romer and Weil, and look for what it takes to maximize the HDI. And they find massive overinvestment into physical and human capital, which saving rates so much higher than what the Golden Rule would call for that consumption is almost reduced to zero. Because consumption is not part of HDI! That looks a crass oversight, as we generally assume, correctly I think, that people care about consumption for their standard of living.
Luminosity as an indicator of economic activity
When working with worldwide data, it si often frustrating that data quality and availability is far from uniform across countries. Especially for developing countries, or those with large informal sectors or notable self-sustenance, we have a very imperfect idea of how much economic activity there is. Hence, looking at other indicators that GDP can give us interesting clues.
Xi Chen and William Nordhaus make the case for luminosity. By looking at how brightly various locations shine at night, it allows you to infer something about economic activity and the level of development. Also, it allows to say something about regional distribution of economic activity. Of course, this is not going to be perfect, especially for developed economies where data is of much better quality to start with.
The standard data set for international macroeconomics data is the Penn World Tables. It also grade grades to its data, telling us how reliable it is. Unfortunately, these grades are largely ignored in empirical work. Chen and Nordhaus ask whether they can increase the quality of output measured with their luminosity data and they claim this is only useful for those labeled D and E. Yet they do not advocate using luminosity data for countrywide analysis. Indeed, data collection methods will eventually improve and traditional data will move up in the quality ladder. Luminosity data is far from perfect, it is just that in some countries official data is even worse at the moment. Chen and Nordhaus are more confident with luminosity as a proxy for regional activity in some cases, even if measurement error is even larger there.
Xi Chen and William Nordhaus make the case for luminosity. By looking at how brightly various locations shine at night, it allows you to infer something about economic activity and the level of development. Also, it allows to say something about regional distribution of economic activity. Of course, this is not going to be perfect, especially for developed economies where data is of much better quality to start with.
The standard data set for international macroeconomics data is the Penn World Tables. It also grade grades to its data, telling us how reliable it is. Unfortunately, these grades are largely ignored in empirical work. Chen and Nordhaus ask whether they can increase the quality of output measured with their luminosity data and they claim this is only useful for those labeled D and E. Yet they do not advocate using luminosity data for countrywide analysis. Indeed, data collection methods will eventually improve and traditional data will move up in the quality ladder. Luminosity data is far from perfect, it is just that in some countries official data is even worse at the moment. Chen and Nordhaus are more confident with luminosity as a proxy for regional activity in some cases, even if measurement error is even larger there.
It is difficult to measure poverty
Measuring poverty is very difficult. First, it is a relative concept and requires the definition of a standard or threshold. Second, as people are usually not normally distributed, any single measure misses some aspect of the distribution. Third, the item whose distribution is measured may not be the appropriate one to represent poverty. Most of the time this is income, but temporary low income is very different from permanent low income, and in both cases, purchasing power may differ dramatically on location, social policies and period. All these difficulties have lead to a plethora of poverty measures. In fact, if you look at the program of any economic inequality conference, there will be plenty of papers on new measures by authors hopeful that their names will stick to a new index or coefficient.
Walter Bossert, Satya Chakravarty and Conchita d'Ambrosio come up with a new measure that emphasizes the persistence of poverty. They are very careful in making their measure following three axioms: the measure corresponds to static poverty in the one period-case, a measure is worse is poverty spells are longer ans spells out of poverty are shorter, and two decomposability axioms too complex to describe here.
The measure they propose is a weighted sum of per period poverty measures, where weight are proportional to the current poverty spell. Using the European Community Household Panel, they find that their measure does not change rankings much whether poverty spell weights are used or not. But I bet they would change quite a bit for the US.
Walter Bossert, Satya Chakravarty and Conchita d'Ambrosio come up with a new measure that emphasizes the persistence of poverty. They are very careful in making their measure following three axioms: the measure corresponds to static poverty in the one period-case, a measure is worse is poverty spells are longer ans spells out of poverty are shorter, and two decomposability axioms too complex to describe here.
The measure they propose is a weighted sum of per period poverty measures, where weight are proportional to the current poverty spell. Using the European Community Household Panel, they find that their measure does not change rankings much whether poverty spell weights are used or not. But I bet they would change quite a bit for the US.
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