Solution and Estimation of Dynamic Discrete Choice Structural Models Using Euler Equations

June 16, 2016

By Victor Aguirregabiria and Arvind Magesan

This paper extends the Euler Equation (EE) representation of dynamic decision problems to a general class of discrete choice models and shows that the advantages of this approach apply not only to the estimation of structural parameters but also to the computation of a solution and to the evaluation of counterfactual experiments. We use a choice probabilities representation of the discrete decision problem to derive marginal conditions of optimality with the same features as the standard EEs in continuous decision problems. These EEs imply a fixed point mapping in the space of conditional choice values, that we denote the Euler equation-value (EE-value) operator. We show that, in contrast to Euler equation operators in continuous decision models, this operator is a contraction. We present numerical examples that illustrate how solving the model by iterating in the EE-value mapping implies substantial computational savings relative to iterating in the Bellman equation (that requires a much larger number of iterations) or in the policy function (that involves a costly valuation step). We define a sample version of the EE-value operator and use it to construct a sequence of consistent estimators of the structural parameters, and to evaluate counterfactual experiments. The computational cost of evaluating this sample-based EE-value operator increases linearly with sample size, and provides an unbiased (in finite samples) and consistent estimator the counterfactual. As such there is no curse of dimensionality in the consistent estimation of the model and in the evaluation of counterfactual experiments. We illustrate the computational gains of our methods using several Monte Carlo experiments.

Interesting approach that is not obvious at first sight. Indeed, why iterate on first order conditions in a discrete choice setup? But it works well.

The Limits of Central Bank Forward Guidance under Learning

June 10, 2016

By Stephen Cole

Central bank forward guidance emerged as a pertinent tool for monetary policymakers since the Great Recession. Nevertheless, the effects of forward guidance remain unclear. This paper investigates the effectiveness of forward guidance while relaxing two standard macroeconomic assumptions: rational expectations and frictionless financial markets. Agents forecast future macroeconomic variables via either the rational expectations hypothesis or a more plausible theory of expectations formation called adaptive learning. A standard Dynamic Stochastic General Equilibrium (DSGE) model is extended to include the financial accelerator mechanism. The results show that the addition of financial frictions amplifies the differences between rational expectations and adaptive learning to forward guidance. The macroeconomic variables are overall more responsive to forward guidance under rational expectations than under adaptive learning. During a period of economic crisis (e.g. a recession), output under rational expectations displays more favorable responses to forward guidance than under adaptive learning. These differences are exacerbated when compared to a similar analysis without financial frictions. Thus, monetary policymakers should consider the way in which expectations and credit frictions are modeled when examining the effects of forward guidance.

Forward guidance is all about expectation formation, thus understanding expectation formation is a pretty big deal if you want to apply such policies. And it matters, as this paper clearly shows.

Challenges for Central Banks’ Macro Models

June 8, 2016

By Jesper Lindé, Frank Smets and Rafael Wouters

In this paper we discuss a number of challenges for structural macroeconomic models in the light of the Great Recession and its aftermath. It shows that a benchmark DSGE model that shares many features with models currently used by central banks and large international institutions has difficulty explaining both the depth and the slow recovery of the Great Recession. In order to better account for these observations, the paper analyses three extensions of the benchmark model. First, we estimate the model allowing explicitly for the zero lower bound constraint on nominal interest rates. Second, we introduce time-variation in the volatility of the exogenous disturbances to account for the non-Gaussian nature of some of the shocks. Third and finally, we extend the model with a financial accelerator and allow for time-variation in the endogenous propagation of financial shocks. All three extensions require that we go beyond the linear Gaussian assumptions that are standard in most policy models. We conclude that these extensions go some way in accounting for features of the Great Recession and its aftermath, but they do not suffice to address some of the major policy challenges associated with the use of non-standard monetary policy and macroprudential policies.

The models of Smets and Wouters are the foundation of many of the models currently used in policy circles. Given that these models have been heavily criticized by some that they are lacking the very features that were relevant in the last crisis, it is interesting to see what Smets and Wouters (and Lindé) have come up with as a response. Given all the other work that has been done by others, and that has in part been highlighted on this blog, the response is disappointing, though. One could have in particular expected a more explicit modeling of the financial sector, for example, or there still seems to be a lot of linearity in the model even with the ZLB. My assessment, however, is based on a very quick reading of the paper, it is 95 pages long after all.

International competition and labor market adjustment

June 3, 2016

By João Paulo Pessoa

How does welfare change in the short- and long-run in high wage countries when integrating with low wage economies like China? Even if consumers benefit from lower prices, there can be significant welfare losses from increases in unemployment and lower wages. I construct a dynamic multi-sector country Ricardian trade model that incorporates both search frictions and labor mobility frictions. I then structurally estimate this model using cross-country sector-level data and quantify both the potential losses to workers and benefits to consumers arising from China’s integration into the global economy. I find that overall welfare increases in northern economies, both in the transition period and in the new steady state equilibrium. In import competing sectors, however, workers bear a costly transition, experiencing lower wages and a rise in unemployment. I validate the micro implications of the model using employer-employee panel data.

Good paper in the context of the current discussion of the virtues of free trade, and in particular the sectoral transition costs.

Housing and Tax-Deferred Retirement Accounts

May 30, 2016

By Anson T. Y. Ho and Jie Zhou

Assets in tax-deferred retirement accounts (TDA) and housing are two major components of household portfolios. In this paper, we develop a life-cycle model to examine the interaction between households’ use of TDA and their housing decisions. The model generates life-cycle patterns of home ownership and the composition of net worth that are broadly consistent with the data from the Survey of Consumer Finances. We find that TDA promotes home ownership, as households take advantage of the preferential tax treatments for both TDA and home ownership. They substitute TDA assets for home equity by accumulating wealth in TDA and making smaller down payments (taking out bigger mortgages); consequently, they become homeowners earlier in their lives. On the other hand, housing-related policies, such as a minimum down payment requirement and mortgage interest deductibility, affect households’ housing decisions more than their use of TDA.

It is no mystery that savings decisions are complex. The authors here address jointly two important savings motives, and they show that they should not be studied separately. This means that looking the impact of policy changes has now become more complex. For example, a simplification of the various TDAs offered in the US will likely have an impact on homeownership. Unfortunately, this means that such studies will need heavy artillery in terms of computing power.

An empirical equilibrium model of a decentralized asset market

May 18, 2016

By Alessandro Gavazza

I estimate a search-and-bargaining model of a decentralized market to quantify the effects of trading frictions on asset allocations, asset prices and welfare, and to quantify the effects of intermediaries that facilitate trade. Using business-aircraft data, I find that, relative to the Walrasian benchmark, 18.3 percent of the assets are misallocated; prices are 19.2-percent lower; and the aggregate welfare losses equal 23.9 percent. Dealers play an important role in reducing trading frictions: In a market with no dealers, a larger fraction of assets would be misallocated, and prices would be higher. However, dealers reduce aggregate welfare because their operations are costly, and they impose a negative externality by decreasing the number of agents’ direct transactions.

That is a pretty cool paper, especially in the current debate about what added value financial brokers and wealth managers actually bring to the table. For this reason, I would have preferred a title like “Do Asset Dealers Contribute to Aggregate Welfare?” Readership would then be an order of magnitude larger.

Optimal Trade Policy, Equilibrium Unemployment and Labor Market Inefficiency

May 13, 2016

By Wisarut Suwanprasert

Why do politicians advocate trade protections to save domestic jobs when neoclassical trade models suggest that small open economies should implement free trade? The novel insight of this paper is that trade protections can be rationalized as a second-best policy that improves the domestic welfare when the equilibrium unemployment is different from the constrain-efficient unemployment. To understand the puzzle, I incorporate a Diamond-Mortensen-Pissarides frictional labor market into the standard Heckscher-Ohlin model of international trade. The model offers four main findings. First, when the relative price of the labor (capital)-intensive good increases, equilibrium unemployment decreases (increases). Second, a labor market in a competitive equilibrium is constrained-efficient when the Hosios condition is satisfied. Third, a capital-abundant country with inefficiently high unemployment may experience welfare losses from trade. Conditional on having the same observed trade share, a labor-abundant country with inefficiently high unemployment have extra welfare gains from international trade. Finally and importantly, when the labor market in a small open economy generates inefficiently high equilibrium unemployment, the optimal trade policy is to raise the domestic price of its labor-intensive goods (an import tariff in a capital-abundant country and an export subsidy in a labor-abundant country). Free trade is optimal only when a labor market is initially efficient. The model predictions are supported by patterns of tariffs in WTO member countries.

VERY timely paper on a topic that economists are thought to have wide agreement on, perhaps wrongly. I am looking forward to the literature this paper will spawn.


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