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 PaperPay, Employment, and Dynamics of Young Firms
July 2019
Working Paper Number:
CES-19-23
Why do young firms pay less? Using confidential microdata from the US Census Bureau, we find lower earnings among workers at young firms. However, we argue that such measurement is likely subject to worker and firm selection. Exploiting the two-sided panel nature of the data to control for relevant dimensions of worker and firm heterogeneity, we uncover a positive and significant young-firm pay premium. Furthermore, we show that worker selection at firm birth is related to future firm dynamics, including survival and growth. We tie our empirical findings to a simple model of pay, employment, and dynamics of young firms.View Full Paper PDF
-
Working PaperEstimating the U.S. Citizen Voting-Age Population (CVAP) Using Blended Survey Data, Administrative Record Data, and Modeling: Technical Report
April 2023
Working Paper Number:
CES-23-21
This report develops a method using administrative records (AR) to fill in responses for nonresponding American Community Survey (ACS) housing units rather than adjusting survey weights to account for selection of a subset of nonresponding housing units for follow-up interviews and for nonresponse bias. The method also inserts AR and modeling in place of edits and imputations for ACS survey citizenship item nonresponses. We produce Citizen Voting-Age Population (CVAP) tabulations using this enhanced CVAP method and compare them to published estimates. The enhanced CVAP method produces a 0.74 percentage point lower citizen share, and it is 3.05 percentage points lower for voting-age Hispanics. The latter result can be partly explained by omissions of voting-age Hispanic noncitizens with unknown legal status from ACS household responses. Weight adjustments may be less effective at addressing nonresponse bias under those conditions.View Full Paper PDF
-
Working PaperPerson Matching in Historical Files using the Census Bureau's Person Validation System
September 2014
Working Paper Number:
carra-2014-11
The recent release of the 1940 Census manuscripts enables the creation of longitudinal data spanning the whole of the twentieth century. Linked historical and contemporary data would allow unprecedented analyses of the causes and consequences of health, demographic, and economic change. The Census Bureau is uniquely equipped to provide high quality linkages of person records across datasets. This paper summarizes the linkage techniques employed by the Census Bureau and discusses utilization of these techniques to append protected identification keys to the 1940 Census.View Full Paper PDF
-
Working PaperExploratory Report: Annual Business Survey Ownership Diversity and Its Association with Patenting and Venture Capital Success
October 2024
Working Paper Number:
CES-24-62
The Annual Business Survey (ABS) as the replacement for the Survey of Business Owners (SBO) serves as the principal data source for investigating business ownership of minorities, women, and immigrants. As a combination of SBO, the innovation questions formerly collected in the Business R&D and Innovation Survey (BRDIS), and an R&D module for microbusinesses with fewer than 10 employees, ABS opens new research opportunities investigating how ownership demographics are associated with innovation. One critical issue that ABS is uniquely able to investigate is the role that diversity among ownership teams plays in facilitating innovation or intermediate innovation outcomes in R&D-performing microbusinesses. Earlier research using ABS identified both demographic and disciplinary diversity as strong correlates to new-to-market innovation. This research investigates the extent to which the various forms of diversity also impact tangible innovation related intermediate outcomes such as the awarding of patents or securing venture capital financing for R&D. The other major difference with the earlier work is the focus on R&D-performing microbusinesses that are an essential input to radical innovation through the division of innovative labor. Evidence that disciplinary and/or demographic diversity affect the likelihood of receiving a patent or securing venture capital financing by small, high-tech start-ups may have implications for higher education, affirmative action, and immigration policy.View Full Paper PDF
-
Working PaperWhat Determines Environmental Performance at Paper Mills? The Roles of Abatement Spending, Regulation, and Efficiency
April 2003
Working Paper Number:
CES-03-10
This paper examines the determinants of environmental performance at paper mills, measured by air pollution emissions per unit of output. We consider differences across plants in air pollution abatement expenditures, local regulatory stringency, and productive efficiency. Emissions are significantly lower in plants with a larger air pollution abatement capital stock: a 10 percent increase in abatement capital stock appears to reduce emissions by 6.9 percent. This translates into a sizable social return: one dollar of abatement capital stock is estimated to provide and annual return of about 75 cents in pollution reduction benefits. Local regulatory stringency and productive efficiency also matter: plants in non-attainment counties have 43 percent lower emissions and plants with 10 percent higher productivity have 2.5 percent lower emissions. For pollution abatement operating costs we find (puzzlingly) positive, but always insignificant, coefficients.View Full Paper PDF
-
Working PaperWho Leaves, Where to, and Why Worrry? Employee Mobility, Employee Entrepreneurship, and Effects on Source Firm Performance
September 2009
Working Paper Number:
CES-09-32
We theorize that differences in human assets' ability to generate value are linked to exit decisions and their effects on firm performance. Using linked employee-employer data from the U.S. Census Bureau on legal services, we find that employees with higher earnings are less likely to leave relative to employees with lower earnings, but if they do leave, they are more likely to move to a spin-out instead of an incumbent firm. Employee entrepreneurship has a larger adverse impact on source firm performance than moves to established firms, even controlling for observable employee quality. Findings suggest that the transfer of human capital, complementary assets, and opportunities all affect mobility decisions and their impact on source firms.View Full Paper PDF
-
Working PaperLong-Run Adult Socio-economic Outcomes from In Utero Airborne Lead Exposure
November 2022
Working Paper Number:
CES-22-53
As a neurotoxin, early exposure to lead has long been assumed to affect socioeconomic out-comes well into adulthood. However, the empirical literature documenting such effects has been limited. This study documents the long-term effects of in utero exposure to air lead on adult socio-economic outcomes, including earnings, disabilities, employment, public assistance, and education, using US survey and administrative data. Specifically, we match individuals in the 2000 US Decennial Census and 2001-2014 American Community Surveys to average lead concentrations in the individual's birth county during his/her 9 months in utero. We find a 0.5 'g/m3 decrease in air lead, representing the average 1975-85 change resulting from the passage of the U.S. Clean Air Act, is associated with an increase in earnings of 3.5%, or a present value, at birth, of $21,400 in lifetime earnings. Decomposing this effect, we find greater exposure to lead in utero is associated with an increase in disabilities in adulthood, an increase in receiving public assistance, and a decrease in employment. Looking at effects by sex, long-term effects for girls seem to fall on participation in the formal labor market, whereas for boys it appears to fall more on hours worked. This is the first study to document such long-term effects from lead using US data. We estimate the present value in 2020, from all earnings impacts from 1975 forward, to be $4,230 Billion using a discount rate of 3%. In 2020 alone, the benefits are $252 B, or about 1.2% of GDP. Thus, our estimates imply the Clean Air Act's lead phase out is still returning a national dividend of over 1% every year.View Full Paper PDF
-
Working PaperENFORCING COVENANTS NOT TO COMPETE: THE LIFE-CYCLE IMPACT ON NEW FIRMS
June 2014
Working Paper Number:
CES-14-27
We examine the impact of enforcing non-compete covenants (CNC) on the formation and performance of new firms using matched employer-employee data on 30 US states. To identify the impact of CNC, we exploit the inter-state variation in CNC enforcement along with the fact that courts do not enforce such covenants between law firms and departing lawyers in any state. Using a difference-in-difference-in-difference specification with law firms and firms that are not withinindustry spinouts as the baseline, we find states with stricter CNC enforcement have fewer, but larger within-industry spinouts that are more likely to survive their nascent years, and conditional on survival, grow faster during those years. These results are consistent with CNC enforcement having a selection effect on within-industry spinouts. Particularly, with stricter enforcement, only founders with higher-quality ideas and resources choose to overcome CNC-related barriers, which reduces entry rate but increases observed short-term performance of these spinouts.View Full Paper PDF
-
Working PaperWhat Do I Take With Me: The Impact of Transfer and Replication of Resources on Parent and Spin-Out Firm Performance
February 2011
Working Paper Number:
CES-11-06
Focusing on entrepreneurial ventures created by employees leaving a firm, our study examines the differential impact of knowledge transfer and knowledge spillovers on both parent and spin-out performance. While extant research often uses knowledge transfer and spillover interchangeably, our study distinguishes between the two based on the 'rivalness' of the relevant knowledge. We theorize that both knowledge transfer (proxied by the size of the exiting employee team) and knowledge spillovers (proxied by the experience of the exiting employee team) will aid spin-out performance. However, knowledge transfer, being more rival, will have a greater adverse impact than knowledge spillovers on parent firm performance. Using U.S. Census Bureau linked employee-employer data from the legal services industry, we find support for our hypotheses. Our study thus contributes to extant literature by highlighting a key dimension of knowledge ' rivalness ' and the differential competitive dynamics effect of resources with varying degrees of rivalness.View Full Paper PDF
-
Working PaperIPO Waves, Product Market Competition, and the Going Public Decision: Theory and Evidence
March 2012
Working Paper Number:
CES-12-07
We develop a new rationale for IPO waves based on product market considerations. Two firms, with differing productivity levels, compete in an industry with a significant probability of a positive productivity shock. Going public, though costly, not only allows a firm to raise external capital cheaply, but also enables it to grab market share from its private competitors. We solve for the decision of each firm to go public versus remain private, and the optimal timing of going public. In equilibrium, even firms with sufficient internal capital to fund their new investment may go public, driven by the possibility of their product market competitors going public. IPO waves may arise in equilibrium even in industries which do not experience a productivity shock. Our model predicts that firms going public during an IPO wave will have lower productivity and post-IPO profitability but larger cash holdings than those going public off the wave; it makes similar predictions for firms going public later versus earlier in an IPO wave. We empirically test and find support for these predictions.View Full Paper PDF
