Analytic Derivatives for Estimation of Linear Dynamic Models
November 1988
Working Paper Number:
CES-88-05
Abstract
This paper develops two algorithms. Algorithm I computes the exact, Gaussian, log-likelihood function, its exact, gradient vector, and an asymptotic approximation of its Hessian matrix, for discrete-time, linear, dynamic models in state-space form. Algorithm 2, derived from algorithm I, computes the exact, sample, information matrix of this likelihood function. The computed quantities are analytic (not numerical approximations) and should, therefore, be useful for reliably, quickly, and accurately: (i) checking local identifiability of parameters by checking the rank of the information matrix; (ii) using the gradient vector and Hessian matrix to compute maximum likelihood estimates of parameters with Newton methods; and, (iii) computing asymptotic covariances (Cramer-Rao bounds) of the parameter estimates with the Hessian or the information matrix. The principal contribution of the paper is algorithm 2, which extends to multivariate models the univariate results of Porat and Friedlander (1986). By relying on the Kalman filter instead of the Levinson-Durbin filter used by Porat and Friedlander, algorithms 1 and 2 can automatically handle any pattern of missing or linearly aggregated data. Although algorithm 1 is well known, it is treated in detail in order to make the paper self contained.
Document Tags and Keywords
Keywords
Keywords are automatically generated using KeyBERT, a powerful and innovative
keyword extraction tool that utilizes BERT embeddings to ensure high-quality and contextually relevant
keywords.
By analyzing the content of working papers, KeyBERT identifies terms and phrases that capture the essence of the
text, highlighting the most significant topics and trends. This approach not only enhances searchability but
provides connections that go beyond potentially domain-specific author-defined keywords.
:
Tags
Tags are automatically generated using a pretrained language model from spaCy, which excels at
several tasks, including entity tagging.
The model is able to label words and phrases by part-of-speech,
including "organizations." By filtering for frequent words and phrases labeled as "organizations", papers are
identified to contain references to specific institutions, datasets, and other organizations.
:
Similar Working Papers
Similarity between working papers are determined by an unsupervised neural
network model
know as Doc2Vec.
Doc2Vec is a model that represents entire documents as fixed-length vectors, allowing for the
capture of semantic meaning in a way that relates to the context of words within the document. The model learns to
associate a unique vector with each document while simultaneously learning word vectors, enabling tasks such as
document classification, clustering, and similarity detection by preserving the order and structure of words. The
document vectors are compared using cosine similarity/distance to determine the most similar working papers.
Papers identified with 🔥 are in the top 20% of similarity.
The 10 most similar working papers to the working paper 'Analytic Derivatives for Estimation of Linear Dynamic Models' are listed below in order of similarity.
-
Working PaperThe Dynamics Of Productivity In The Telecommunications Equipment Industry
February 1992
Working Paper Number:
CES-92-02
Technological change and deregulation have caused a major restructuring of the telecommunications equipment industry over the last two decades. We estimate the parameters of a production function for the equipment industry and then use those estimates to analyze the evolution of plant-level productivity over this period. The restructuring involved significant entry and exit and large changes in the sizes of incumbents. Since firms choices on whether to liquidate and the on the quantities of inputs demanded should they continue depend on their productivity, we develop an estimation algorithm that takes into account the relationship between productivity on the one hand, and both input demand and survival on the other. The algorithm is guided by a dynamic equilibrium model that generates the exit and input demand equations needed to correct for the simultaneity and selection problems. A fully parametric estimation algorithm based on these decision rules would be both computationally burdensome and require a host of auxiliary assumptions. So we develop a semiparametric technique which is both consistent with a quite general version of the theoretical framework and easy to use. The algorithm produces markedly different estimates of both production function parameters and of productivity movements than traditional estimation procedures. We find an increase in the rate of industry productivity growth after deregulation. This in spite of the fact that there was no increase in the average of the plants' rates of productivity growth, and there was actually a fall in our index of the efficiency of the allocation of variable factors conditional on the existing distribution of fixed factors. Deregulation was, however, followed by a reallocation of capital towards more productive establishments (by a down sizing, often shutdown, of unproductive plants and by a disproportionate growth of productive establishments) which more than offset the other factors' negative impacts on aggregate productivity.View Full Paper PDF
-
Working PaperTechnology Lock-In and Costs of Delayed Climate Policy
July 2023
Working Paper Number:
CES-23-33
This paper studies the implications of current energy prices for future energy efficiency and climate policy. Using U.S. Census microdata and quasi-experimental variation in energy prices, we first show that manufacturing plants that open when electricity prices are low consume more energy throughout their lifetime, regardless of current electricity prices. We then estimate that a persistent bias of technological change toward energy can explain the long-term effects of entry-year electricity prices on energy intensity. Overall, this 'technology lock-in' implies that increasing entry-year electricity prices by 10% would decrease a plant's energy intensity of production by 3% throughout its lifetime.View Full Paper PDF
-
Working PaperWhittling Away At Productivity Dispersion
March 1995
Working Paper Number:
CES-95-05
In any time period, in any industry, plant productivity levels differ widely and this dispersion is persistent. This paper explores the sources of this dispersion and their relative magnitudes in the textile industry. Plants that are measured as being more productive but pay higher wages are not necessarily more profitable; wage dispersion can account for approximately 15 percent of productivity dispersion. A plant that is highly productive today may not be as productive tomorrow. I develop a new method for measuring ex-ante dispersion and the percentage of dispersion "explained" by mean reversion. Mean reversion accounts for as much as one half the observed productivity dispersion. A portion of the dispersion, however, appears to reflect real quality differences between plants; plants that are measured as being more productive expand faster and are less likely to exit.View Full Paper PDF
-
Working PaperWho are the people in my neighborhood? The 'contextual fallacy' of measuring individual context with census geographies
February 2018
Working Paper Number:
CES-18-11
Scholars deploy census-based measures of neighborhood context throughout the social sciences and epidemiology. Decades of research confirm that variation in how individuals are aggregated into geographic units to create variables that control for social, economic or political contexts can dramatically alter analyses. While most researchers are aware of the problem, they have lacked the tools to determine its magnitude in the literature and in their own projects. By using confidential access to the complete 2010 U.S. Decennial Census, we are able to construct'for all persons in the US'individual-specific contexts, which we group according to the Census-assigned block, block group, and tract. We compare these individual-specific measures to the published statistics at each scale, and we then determine the magnitude of variation in context for an individual with respect to the published measures using a simple statistic, the standard deviation of individual context (SDIC). For three key measures (percent Black, percent Hispanic, and Entropy'a measure of ethno-racial diversity), we find that block-level Census statistics frequently do not capture the actual context of individuals within them. More problematic, we uncover systematic spatial patterns in the contextual variables at all three scales. Finally, we show that within-unit variation is greater in some parts of the country than in others. We publish county-level estimates of the SDIC statistics that enable scholars to assess whether mis-specification in context variables is likely to alter analytic findings when measured at any of the three common Census units.View Full Paper PDF
-
Working PaperJob Creation, Small vs. Large vs. Young, and the SBA
September 2015
Working Paper Number:
CES-15-24
Analyzing a list of all Small Business Administration (SBA) loans in 1991 to 2009 linked with annual information on all U.S. employers from 1976 to 2012, we apply detailed matching and regression methods to estimate the variation in SBA loan effects on job creation and firm survival across firm age and size groups. The estimated number of jobs created per million dollars of loans within the small business sector generally increases with size and decreases in age. The results suggest that the growth of small, mature firms is least financially constrained, and that faster growing firms experience the greatest financial constraints to growth. The estimated association between survival and loan amount is larger for younger and smaller firms facing the 'valley of death.'View Full Paper PDF
-
Working PaperTechnology Locks, Creative Destruction And Non-Convergence In Productivity Levels
April 1995
Working Paper Number:
CES-95-06
This paper presents a simple solution to a new model that seeks to explain the distribution of plants across productivity levels within an industry, and empirically confirms some key predictions using the U.S. textile industry. In the model, plants are locked into a given productivity level, until they exit or retool. Convex costs of adjustment captures the fact that more productive plants expand faster. Provided there is technical change, productivity levels do not converge; the model achieves persistent dispersion in productivity levels within the context of a distortion free competitive equilibrium. The equilibrium, however, is rather turbulent; plants continually come on line with the cutting edge technology, gradually expand and finally exit or retool when they cease to recover their variable costs. The more productive plants create jobs, while the less productive destroy them. The model establishes a close link between productivity growth and dispersion in productivity levels; more rapid productivity growth leads to more widespread dispersion. This prediction is empirically confirmed. Additionally, the model provides an explanation for S-shaped diffusion.View Full Paper PDF
-
Working PaperLocation, Location, Location: The 3L Approach to House Price Determination
May 2004
Working Paper Number:
CES-04-06
The immobility of houses means that their location affects their values. This explains the common belief that three things determine the price of a house: location, location, and location. We use this notion to develop the 3L Approach to house price determination. That is, prices are determined by the Metropolitan Statistical Area (MSA), town, and street where the house is located. This study creates a unique data set based on data from the American Housing Survey (AHS) consisting of small 'clusters' of housing units with information on their housing characteristics and resident characteristics that is merged with census tract-level attributes. We use this data to verify the 3L Approach: we find that all three levels of location are significant when estimating the house price hedonic equation. This indicates that individuals care about their local neighborhood, i.e. the general upkeep of their street and possibly their neighbors' characteristics (cluster variables), a broader area such as the school district and/or the town (tract variables) that account for school quality and crime rates, and the particular amenities found in their MSA.View Full Paper PDF
-
Working PaperThe Industrial Revolution in Services
October 2021
Working Paper Number:
CES-21-34
The U.S. has experienced an industrial revolution in services. Firms in service industries, those where output has to be supplied locally, increasingly operate in more markets. Employment, sales, and spending on fixed costs such as R&D and managerial employment have increased rapidly in these industries. These changes have favored top firms the most and have led to increasing national concentration in service industries. Top firms in service industries have grown entirely by expanding into new local markets that are predominantly small and mid-sized U.S. cities. Market concentration at the local level has decreased in all U.S. cities but by significantly more in cities thatwere initially small. These facts are consistent with the availability of a new menu of fixed-cost-intensive technologies in service sectors that enable adopters to produce at lower marginal costs in any markets. The entry of top service firms into new local markets has led to substantial unmeasured productivity growth, particularly in small markets.View Full Paper PDF
-
Working PaperProductivity Races II: The Issue of Capital Measurement
January 1997
Working Paper Number:
CES-97-03
This paper explores the role of capital measurement in determining the productivity of individual textile plants. In addition to gross book value of capital, we experiment with a perpetual inventory measure of capital and implicit (estimated) deflator associated with the age of the plant. Following the methodology of the earlier paper (Productivity Races I), we find that measures of productivity constructed from different measures of capital are highly correlated. Further, their association with alternative measures of economic performance is approximately the same. Nevertheless, the perpetual inventory measure of capital -- the most desirable measure from a theoretical perspective -- does consistently outperform the other two measures.View Full Paper PDF
-
Working PaperARE FIXED EFFECTS FIXED? Persistence in Plant Level Productivity
May 1996
Working Paper Number:
CES-96-03
Estimates of production functions suffer from an omitted variable problem; plant quality is an omitted variable that is likely to be correlated with variable inputs. One approach is to capture differences in plant qualities through plant specific intercepts, i.e., to estimate a fixed effects model. For this technique to work, it is necessary that differences in plant quality are more or less fixed; if the "fixed effects" erode over time, such a procedure becomes problematic, especially when working with long panels. In this paper, a standard fixed effects model, extended to allow for serial correlation in the error term, is applied to a 16-year panel of textile plants. This parametric approach strongly accepts the hypothesis of fixed effects. They account for about one-third of the variation in productivity. A simple non-parametric approach, however, concludes that differences in plant qualities erode over time, that is plant qualities f-mix. Monte Carlo results demonstrate that this discrepancy comes from the parametric approach imposing an overly restrictive functional form on the data; if there were fixed effects of the magnitude measured, one would reject the hypothesis of f-mixing. For textiles, at least, the functional form of a fixed effects model appears to generate misleading conclusions. A more flexible functional form is estimated. The "fixed" effects actually have a half life of approximately 10 to 20 years, and they account for about one-half the variation in productivity.View Full Paper PDF
