"The data used by economists can be broadly divided into two categories. First, structured datasets arise when a government agency, trade association, or company can justify the expense of assembling records. The Internet has transformed how economists interact with these datasets by lowering the cost of storing, updating, distributing, finding, and retrieving this information. Second, some economic researchers affirmatively collect data of interest. For researcher-collected data, the Internet opens exceptional possibilities both by increasing the amount of information available for researchers to gather and by lowering researchers' costs of collecting information. In this paper, I explore the Internet's new datasets, present methods for harnessing their wealth, and survey a sampling of the research questions these data help to answer. The first section of this paper discusses "scraping" the Internet for data—that is, collecting data on prices, quantities, and key characteristics that are already available on websites but not yet organized in a form useful for economic research. A second part of the paper considers online experiments, including experiments that the economic researcher observes but does not control (for example, when Amazon or eBay alters site design or bidding rules); and experiments in which a researcher participates in design, including those conducted in partnership with a company or website, and online versions of laboratory experiments. Finally, I discuss certain limits to this type of data collection, including both "terms of use" restrictions on websites and concerns about privacy and confidentiality."

"In this paper, we tackle the problem of prediction and confidence intervals for time series using a statistical learning approach and quantile loss functions. In a first time, we show that the Gibbs estimator (also known as Exponentially Weighted aggregate) is able to predict as well as the best predictor in a given family for a wide set of loss functions. In particular, using the quantile loss function of Koenker and Bassett (1978), this allows to build confidence intervals. We apply these results to the problem of prediction and confidence regions for the French Gross Domestic Product (GDP) growth, with promising results."

"In this paper we tackle the problem of fast rates in time series forecasting from a statistical learning perspective. In a serie of papers (e.g. Meir 2000, Modha and Masry 1998, Alquier and Wintenberger 2012) it is shown that the main tools used in learning theory with iid observations can be extended to the prediction of time series. The main message of these papers is that, given a family of predictors, we are able to build a new predictor that predicts the series as well as the best predictor in the family, up to a remainder of order $1/sqrt{n}$. It is known that this rate cannot be improved in general. In this paper, we show that in the particular case of the least square loss, and under a strong assumption on the time series (phi-mixing) the remainder is actually of order $1/n$. Thus, the optimal rate for iid variables, see e.g. Tsybakov 2003, and individual sequences, see cite{lugosi} is, for the first time, achieved for uniformly mixing processes. We also show that our method is optimal for aggregating sparse linear combinations of predictors."

--- Assumes observations are in the interval [-B,B] and gets a bound which is O(B^3), and so useless for our purposes.

"The business cycle is a fundamental yet elusive concept in macroeconomics. In this paper, we consider the problem of measuring the business cycle. First, we argue for the output-gap view that the business cycle corresponds to transitory deviations in economic activity away from a permanent, or trend, level. Then we investigate the extent to which a general model-based approach to estimating trend and cycle for the U.S. economy leads to measures of the business cycle that reflect models versus the data. We find empirical support for a nonlinear time series model that produces a business cycle measure with an asymmetric shape across NBER expansion and recession phases. Specifically, this business cycle measure suggests that recessions are periods of relatively large and negative transitory fluctuations in output. However, several close competitors to the nonlinear model produce business cycle measures of widely differing shapes and magnitudes. Given this model-based uncertainty, we construct a model-averaged measure of the business cycle. This measure also displays an asymmetric shape and is closely related to other measures of economic slack such as the unemployment rate and capacity utilization."
--- Worthy, but at the same time makes me want to lock them in a room with a copy of Li and Racine's _Nonparametric Econometrics_, or even _The Elements of Statistical Learning_, and not let them out until they understand it.

"Vapnik-Chervonenkis (VC) dimension is a fundamental measure of the generalization capacity of learning algorithms. However, apart from a few special cases, it is hard or impossible to calculate analytically. Vapnik et al. [10] proposed a technique for estimating the VC dimension empirically. While their approach behaves well in simulations, it could not be used to bound the generalization risk of classifiers, because there were no bounds for the estimation error of the VC dimension itself. We rectify this omission, providing high probability concentration results for the proposed estimator and deriving corresponding generalization bounds."

"In this paper we present a Bernstein-type tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that is not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing sequences. The result is then used to derive asymptotic moderate deviation results. Applications are given for classes of Markov chains, iterated Lipschitz models and functions of linear processes with absolutely regular innovations." Also: http://arxiv.org/abs/0902.0582

"We study the generalization performance of arbitrary online learning algorithms trained on samples coming from a dependent source of data. We show that the generalization error of any stable online algorithm concentrates around its regret--an easily computable statistic of the online performance of the algorithm--when the underlying ergodic process is $beta$- or $phi$-mixing. We show high probability error bounds assuming the loss function is convex, and we also establish sharp convergence rates and deviation bounds for strongly convex losses and several linear prediction problems such as linear and logistic regression, least-squares SVM, and boosting on dependent data. In addition, our results have straightforward applications to stochastic optimization with dependent data, and our analysis requires only martingale convergence arguments; we need not rely on more powerful statistical tools such as empirical process theory."

"Let $(Y_k)$ be a stationary sequence on a probability space taking values in a standard Borel space. Consider the associated maximum likelihood estimator with respect to a parametrized family of Hidden Markov models such that the law of the observations $(Y_k)$ is not assumed to be described by any of the Hidden Markov models of this family. In this paper we investigate the consistency of this estimator in such mispecified models under mild assumptions."

"We study the problem of estimating an unknown function from ergodic samples corrupted by additive noise. It is shown that one can consistently recover an unknown measurable function in this setting, if the one-dimensional (1-D) distribution of the samples is comparable to a known reference distribution, and the noise is independent of the samples and has known mixing rates. The estimates are applied to deterministic sampling schemes, in which successive samples are obtained by repeatedly applying a fixed map to a given initial vector, and it is then shown how the estimates can be used to reconstruct an ergodic transformation from one of its trajectories"

The methodological ideas here are suspect.  It is true that there is not much to predict about an in-control system, and what is happening is largely random and so unpredictable, so that even the true model would show low forecasting ability.  The question however is why we are supposed to think that the DSGE _does_ give us good information about counterfactuals.  If you could show that it had much better predictive performance than baselines like constants or random walks during _out-of-control_ periods, that would be something; but they don't.

"Chains of infinite order are generalizations of Markov chains that constitute a flexible class of models in the general theory of stochastic processes. These processes can be naturally studied using approximating Markov chains. Here we derive new upper bounds for the $bar{d}$-distance and the K"ullback-Leibler divergence between chains of infinite order and their canonical $k$-step Markov approximations. In contrast to the bounds available in the literature our results apply to chains of infinite order compatible with general classes of probability kernels. In particular, we allow kernels with discontinuities and null transition probabilities.""  (Pedantry: Pretty sure Kullback did not spell his name with an umlaut!)

It's a little boggling that they don't cite any of the modern (2000--) work on theoretical properties of CV, but oh well...

Worth reading?

"characterizing learnability is the most basic question of statistical learning theory. A fundamental and long-standing answer, at least for the case of supervised classification and regression, is that learnability is equivalent to uniform convergence of the empirical risk to the population risk, and that if a problem is learnable, it is learnable via empirical risk minimization. In this paper, we consider the General Learning Setting (introduced by Vapnik), which includes most statistical learning problems as special cases. We show that in this setting, there are non-trivial learning problems where uniform convergence does not hold, empirical risk minimization fails, and yet they are learnable using alternative mechanisms. Instead of uniform convergence, we identify stability as the key necessary and sufficient condition for learnability. ... the conditions for learnability in the general setting are significantly more complex than in supervised classification and regression."

Sounded more interesting from the abstract, but still worthwhile.

As I was saying.

"challenges the mainstream paradigm, which is based on the inter-temporal optimisation of welfare by individual agents. It introduces a new methodology for studying how it is institutions which create flows of income, expenditure and production together with stocks of assets (including money) and liabilities, thereby determining how whole economies evolve through time. Starting with extremely simple stock flow consistent (SFC) models, the text describes a succession of increasingly complex models. Solutions of these models are used to illustrate ways in which whole economies evolve when shocked in various ways. Readers will be able to download all the models and explore their properties for themselves. A major conclusion is that economies require management via fiscal and monetary policy if full employment without inflation is to be achieved."  In library.

Solow's prepared remarks for testifying before Congress about modern macro.  To put it in "shorter" form: "I helped invent macroeconomics, and let me assure you that this was not what we had in mind."

Oooh: "We show that if X is a complete separable metric space and C is a countable family of Borel subsets of with finite VC dimension, then, for every stationary ergodic process with values in X, the relative frequencies of sets c \in C converge uniformly to their limiting probabilities. Beyond ergodicity, no assumptions are imposed on the sampling process, and no regularity conditions are imposed on the elements of C. The result extends existing work of Vapnik and Chervonenkis, among others, who have studied uniform convergence for i.i.d. and strongly mixing processes. Our method of proof is new and direct: it does not rely on symmetrization techniques, probability inequalities or mixing conditions. The uniform convergence of relative frequencies for VC-major and VC-graph classes of functions under ergodic sampling is established as a corollary of the basic result for sets."  No rates, but very nice.

Does the overhead bit prevent us from applying? 6 pp. by 31 July would not be a problem.

"how to extract a hypothesis with small risk from the ensemble of hypotheses generated by an arbitrary on-line learning algorithm run on [IID data]. ... a simple large deviation argument [proves] tight data-dependent bounds for the risk of this hypothesis in terms of an easily computable statistic Mn associated with the on-line performance of the ensemble. Via sharp pointwise bounds on Mn, we then obtain risk tail bounds for kernel perceptron algorithms in terms of the spectrum of the empirical kernel matrix. ... A distinctive feature of our approach is that the key tools for our analysis come from the model of prediction of individual sequences; i.e., a model making no probabilistic assumptions on the source generating the data. In fact, these tools turn out to be so powerful that we only need very elementary statistical facts to obtain our final risk bounds." Bounced off this 2004; try again.

"On the critical question of how to portray the industrial sector, I submit the below historical document..."

"With these basic concepts, plus sufficient scribbled arrows, more or less any problem in monetary economics can be solved, up to the level of accuracy of any other model."

I have just advised D.M. to use a copy of this figure in his dissertation proposal.

"Much has been made of the failure of modern macroeconomics to predict or understand the Great Recession of 2007–2009. In this MACRO FOCUS, our resident time-series econo- metrician, James Morley*, explains what is currently meant by “modern” macroeconomics, what is behind its failure, and what can be done to rehabilitate its reputation."

Published version: http://dx.doi.org/10.1007/s10994-011-5268-1

Odd that they don't mention Domingos's "proces-oriented evaluation".

On the connection between linear state-space models and reproducing-kernel Hilbert spaces. (Time to re-read Wahba?)

I will be fascinated to see what of this is "Bayesian".

I find it interesting that the economic/dynamic programming nature of the DSGEs plays no role at all in the argument; all of the work is done by the effective linear model for the observables and latent "shocks" (their Eq. (1)). So this is really about the identifiability of state-space models.

Sounds promising, but much depends on the model, about which he is vague here.

Ans.: nothing and no one; it "deserves to be buried".

""the claim that `modern macro' somehow has the special virtue of following theprinciples of economic theory is tendentious and misleading... The otherpossible defense of modern macro is that, however special it may seem, it isjustified empirically. This too strikes me as a delusion.""

I think you mis-spelled "smoothing spline". HTH. HAND.

My reaction to the first half is "preach it, brothers and sisters!" Perhaps inevitably, the constructive proposals of the 2nd half are less compelling.

The key part is the observation that there is NO POWER to detect reasonably-sized deviations from random walks in only forty years' of data.

Damn.

"Inference about an impulse response is a multiple testing problem with serially correlated coefficient estimates. This paper provides a method to construct simultaneous confidence regions for impulse responses and conditional bands to examine significance levels of individual impulse response coefficients given propagation trajectories. The paper also shows how to constrain a subset of impulse response paths to anchor structural identification and how to formally test the validity of such identifying constraints. Simulation and empirical evidence illustrate the new techniques. A broad summary of asymptotic analytic formulas is provided to make the methods easy to implement with commonly available statistical software."

"The statistical learning theory of risk minimization depends heavily on probability bounds for uniform deviations of the empirical risks. Classical probability bounds using Hoeffding's inequality cannot accommodate more general situations with unbounded loss and dependent data. The current paper introduces an inequality that extends Hoeffding's inequality to handle these more general situations. We will apply this inequality to provide probability bounds for uniform deviations in a very general framework, which can involve discrete decision rules, unbounded loss, and a dependence structure that can be more general than either martingale or strong mixing". --- This is very sweet. The dependence measure they use is, I think, the same as the "gamma' dependence coefficient of Dedecker et al., from their recent book _Weak Dependence_, though apparently independent here.

Why hadn't I seen this before?

Cute 1992 paper on extending uniform laws of large numbers (e.g. for VC classes) to uniform ergodic theorems for mixing processes. I suspect the mixing assumption could be lifted (though ergodicity is essential)