Category A COMPANION TO Theoretical Econometrics

Nonlinear models

Outside of the normal distribution, conditional expectations are typically nonlinear, and in general one would imagine that these infeasible optimal forecasts would be nonlinear functions of past data. The main difficulty that arises with nonlinear forecasts is choosing a feasible forecasting method that performs well with the fairly short historical time series available for macroeconomic forecasting. With many parameters, approximation error in (27.2) is reduced, but estimation error can be increased. Many nonlinear forecasting methods also pose technical prob­lems, such as having objective functions with many local minima, having para­meters that are not globally identified, and difficulties with generating internally consistent й-step ahead forecasts from one-step ahead models.


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Parametric Models

In empirical research we may wish to investigate the dependence of individual hazard functions on exogenous variables. These variables, called the control variates, depict in general various individual characteristics. Let us point out a few examples. In the job search analysis, a typical control variate is the amount of unemployment benefits, which influences the effort of unemployed individuals devoted to the job search and consequently the duration of unemployment. Empirical findings also suggest that family support provided by the state influ­ences the birth rate, and that the expected increase of the insurance premium has an effect on the frequency of declared car accidents...

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The Stochastic Frontier Model with Panel Data

3.1 Time-invariant efficiency

It is increasingly common to use panel data13 in the classical econometric analysis of the stochastic frontier model. Some of the statistical problems (e. g. incon­sistency of point estimates of firm specific efficiency) of classical analysis are alleviated with panel data and the assumption of a particular distributional form for the inefficiency distribution can be dispensed with at the cost of assuming time-invariant efficiencies (i. e. treating them as "individual effects"). Schmidt and Sickles (1984) is an early influential paper which develops a relative efficiency measure based on a fixed effects specification and an absolute efficiency measure based on a random effects specification...

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Moving Average Models

3.2 The traditional approach

A moving average model of order q, denoted by MA(q):


yt = a0 + X akzt-k + £t, ^ ~ NI(0, a2), t Є T, (28.18)


is traditionally viewed as a DGM with a normal white noise process {et, t Є T} (see (28.4)) as the input and {yt, t Є T}, as the output process.

The question which naturally arises at this stage is "how does the DGM (28.18) fit into the orthogonal decomposition given in (28.9)?" A naive answer will be yt = E(yt | o(et-1, et-2,…, et-q)) + et, t Є T. However, such an answer is misleading because operational conditioning cannot be defined in terms of an unobserved stochastic process {et, t Є T}. In view of this, the next question is "how is the formulation (28...

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Multiple tests and levels of significance

It is notable that many tests of the seasonal unit root null hypothesis involve tests on multiple coefficients. In particular, for the application of the HEGY test (31.44),

Hylleberg et al. (1990) recommend that one-sided tests of п1 and п 2 should be applied, with (п 3, п4) either tested sequentially or jointly. The rationale for apply­ing one-sided tests for п 1, п 2, and п 3 is that it permits a test against stationarity, which is not the case when a joint F-type test is applied. Thus, the null hypo­thesis is rejected against stationarity only if the null hypothesis is rejected for each of these three tests...

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The Dynamic Multinomial Choice Model

In this section we present an example of Bayesian inference for dynamic discrete choice models using the Geweke-Keane method of replacing the future compo­nent of the value function with a flexible polynomial function. The discussion is based on a model that is very similar to ones analyzed by Keane and Wolpin (1994, 1997).

In the model we consider, i = 1,…, N agents choose among j = 1,…, 4 mutually exclusive alternatives in each of t = 1,…, 40 periods. One can think of the first two alternatives as work in one of two occupations, the third as attend­ing school and the fourth alternative as remaining at home. One component of the current period payoff in each of the two occupational alternatives is the associated wage, wijt (j = 1, 2). The log-wage equation is:

ln wijt = P0j + e1jXi1t + ...

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