Dynamic factor analysis r example. Constraints for model fitting.

Dynamic factor analysis r example 2003). The function performs maximum-likelihood factor analysis on a covariance matrix or data matrix. 4) SVARs with Factors: FAVAR . One classical assumption of FA is the Title Bayesian Dynamic Factor Analysis (DFA) with 'Stan' Version 1. 1080/00273171. Those methods, however, could not estimate f t directly and thus could not be used for forecasting. The latter two packages additionally support The function produces the variable matrices of dynamic factor models (DFM) with measurement equation x_t = \lambda f_t + u_t, where x_t is an M \times 1 vector of observed variables, f_t is an N \times 1 vector of unobserved factors and \lambda is the corresponding M \times N matrix of factor loadings. We follow the spirit of the approximate dynamic factor model proposed by Chamberlain and Rothschild and allow cross-row and cross-column correlations. 2. Though these examples have an eco-logical focus, the analysis of multivariate time series models is cross-disciplinary work and researchers in other fields will likely benefit from these examples. Dynamic Analysis •Analysis of the properties of a running program •Static analysis typically finds properties that hold of all executions •Dynamic analysis finds properties that hold of one or more executions •Can't prove a program satisfies a particular property •But can detect violations and provide useful information Dynamic Panel Model Consider a simple dynamic panel data model: Y it = ˆY it 1 + i + U it; (2) where U it ˘iid (0;1) and i represents theunobservedindividual heterogeneity. Although DFA is used widely in econometric and psychological fields, it has not been used in fisheries and aquatic sciences to the best of our knowledge. 1 Dynamic Factor Models: Specification and Estimation . Dec 29, 2019 · This document is an informal introduction to—and a subsequent literature review of—[residual] dynamic structural equation modeling ([R]DSEM) of (intensive) longitudinal data. 2003; Muñoz-Carpena et al For example, Forni et al. DFA is conceptually different than what we have been doing in the previous applications. F_qml: T \times r matrix of quasi-maximum likelihood factor estimates - obtained by iteratively Kalman Filtering and Smoothing the factor estimates until EM convergence. Consider this simple model, consisting of a mean \(\mu\) plus error 1 Overview. A Factor Analysis approaches data reduction in a fundamentally different way. We have chosen to divide the process into 4 main steps: 1) constructing See the User Guide chapter on Dynamic Factor Analysis for examples of of using form="dfa". e. DYNAMIC FACTOR MODELS: IDENTIFICATION CONDITIONS We consider a dynamic factor model featuring a dynamic factor representation of the observables and a law of motion for the factors given by a VAR (h) process. (2023). In the context of our motivating H3N2 example, FA maps the observed high-dimensional gene expression data to a latent low-dimensional pathway expression representation (Carvalho et al. 3. and Geweke (1977) were amongst the first to apply the dynamic factor approach to macroeconomic analysis. Using the same notation as in Bai and Ng (2007), the model is given by (1) and (2): %t = Ao ft + Ai/,_i + • • • + A sft-s + et, (1) putational basis used by the dynr R package, and present two illustrative examples to demonstrate the unique features of dynr. These indices are frequently compared to benchmark values Oct 7, 2024 · Compared to nonparametric methods, a major benefit of using a probabilistic approach to quantile factor analysis is the ability to incorporate numerous flexible modeling features. For example, in traditional factor models, an active literature suggests Bayesian priors that shrink the loadings and help select the number of factors. DFA is a statistical multiway analysis technique 1 , where quantitative “units x variables x times” arrays are considered: Jul 9, 2020 · Spatial dynamic factor analysis is a model-based approach for estimating spatiotemporal density dependence in community dynamics rdrr. " In this paper we attempt to address these weaknesses with scenario analysis by embedding it within a dynamic factor model for the underlying risk factors. Dynamic-factor models are flexible models for multivariate time series in which unobserved factors have a The aim of the paper is to develop a procedure able to implement Dynamic Factor Analysis (DFA henceforth) in STATA. Plot the loadings from a DFA Usage plot_loadings( rotated_modelfit, names = NULL, facet = TRUE, violin = TRUE, conf_level = 0. The objective is to help the user at each step of the forecasting process, starting with the construction of a database, all Applies dynamic structural equation models to time-series data with generic and simplified specification for simultaneous and lagged effects. 7) Other High-Dimensional Forecasting Methods . The package is not geared at any specific application, and can be used for dimensionality reduction, forecasting and nowcasting systems of time seri For example, recall our analyses of Pacific harbor seals x t =x t−1 +u+ w t y • Dynamic Factor Analysis (DFA) is an approach to ts modeling that does just that The Dynamic Factor Analysis model in MARSS is The argument form="marxss" in a MARSS() function call specifies a MAR-1 model with eXogenous variables model. Structural VAR identification based on timing restrictions, long run restrictions, and restrictions on factor loadings are discussed and practical computational methods suggested. Thus, for i = 1…n and t = 1…T, x it is decomposed into the sum of two mutually orthogonal unobserved components: the common component, \(\chi _{it}= \boldsymbol \lambda _i^{\prime }\boldsymbol f_{t}\), and the idiosyncratic component, ξ it = μ i + e it. Comparison with Other R Packages. See more examples of recipes below! Check out related publications! Photo credit goes to Twitter @robert_trirop. m: example script to estimate a dynamic factor model (DFM) for a panel of weekly and monthly data using Swiss data from macroeconomicdata. Mapping of time series to trends is done via estimated factor loadings—these allow each time Building on the framework established by Wang et al. The standard (and default) DFA model has B="identity". A main motivation for the use of such models is the so-called “curse of dimensionality” plagueing modeling of high dimensional time series by “ordinary” multivariate AR or ARMA models: For instance, consider an AR system for a, say, 20-dimensional Jun 9, 2024 · Introduction to dfms Sebastian Krantz 2024-06-09. A dynamic factor model with q factors can be written as a static factor model with r factors, where r is finite. This latent variable cannot be directly measured with a single variable (think: intelligence, social anxiety, soil health). head (df_agg) # print df_agg # # a tibble: 6 × 27 # q1 q2 q3 q4 q5 q6 q7 q8 q9 q10 q11 q12 q13 q14 q15 q16 q17 q18 q19 q20 q21 q22 q23 q24 q25 n perc # <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <lgl> <int> <dbl> # 1 false false false false false false false false false false false false false used to estimate the common part in high-dimensional dynamic factor models. 1 The Model Let yt be an m-dimensional vector of observed time series generated by an r-dimensional vector of unobserved common Dynamic Factor Analysis with STATA Alessandro Federici Department of Economic Sciences University of Rome La Sapienza alessandro. Dynamic factor analysis is a dimension reduction tool for multivariate time series. Apr 25, 2021 · The estimation of such common factors can be done using so-called factor analytical models, which have the form \[x_t = \lambda f_t + u_t,\] where \(x_t\) is an \(M\) -dimensional vector of observable variables, \(f_t\) is an \(N \times 1\) vector of unobserved factors, \(\lambda\) is an \(M \times N\) matrix of factor loadings and \(u_t\) is Dynamic factor models (DFMs) postulate that a small number of latent factors explain the common dynamics of a larger number of observed time series (Stock & Watson,2016). Jun 12, 2023 · Factor Analysis (FA) is a statistical method that is used to analyze the underlying structure of a set of variables. Nov 1, 2003 · Dynamic factor analysis can reveal the dynamic characteristics of time series using underlying factors (dynamic factors: DFs) extracted from time series (Zuur et al. A object of class marssMLE. \Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm," Finance and Economics Discussion Series 2024-086. It is used in certain macroeconomic models. Here we will use MARSS to do Dynamic Factor Analysis (DFA), which allows us to look for a set of common underlying processes among a relatively large set of time series (Zuur et al. For example, all married men will have higher expenses … Continue reading Exploratory Factor Analysis in R May 29, 2024 · See the User Guide chapter on Dynamic Factor Analysis for examples of of using form="dfa". The MARSS model Title Bayesian Dynamic Factor Analysis (DFA) with 'Stan' Version 1. data-rich dsge vs. n_factors Number of In econometrics, a dynamic factor (also known as a diffusion index) is a series which measures the co-movement of many time series. Dynamic Factor Analysis Source: vignettes/MARSS_TMB. 2 Principal component analysis and the exact factor model 9 3 The approximate factor model and the blessing of dimensionality 12 4 The generalised dynamic factor model - Time domain 23 5 The generalised dynamic factor model - Frequency domain 26 6 The approximate dynamic factor model in state-space form 35 the number of dynamic factors and tests for the factor restrictions imposed on the VAR. The Dynamic Factor Model The dynamic factor model represents the evolution of a vector of N observed time series, Xt, in terms of a reduced number of unobserved common factors which evolve over time, plus of dynamic factor models in macroeconometrics. These common dynamic factors are driven by the common structural economic shocks, which are the relevant shocks that one must identify for the purposes of conducting policy analysis. See the chapter on DFAs in the ATSA book. Dynamic Factor Modeling is akin to PCA (Principal Components Analysis) for time series data. 2003 ) . initial_variance. For some ecological processes—particularly those with high variability—random walks may be too constraining, while for others, using a random walk scripts/load_process_DFM_switzerland. The notation rk(A) refers to the rank data-rich dsge model: posterior estimates. Factor models generally try to find a small number of unobserved “factors” that influence a substantial portion of the variation in a larger number of observed variables, and they are related to dimension-reduction techniques such as principal components analysis. A: r \times rp factor transition The paper develops a procedure able to implement the Dynamic Factor Analysis in STATA: this methodology manages to combine, from a descriptive point of view (not probabilistic), the cross-section analysis through Principal Component Analysis and the time series dimension of data through linear regression model. developed a non-parametric DFM procedure in the frequency domain, based on dynamic principal components, and Bai provided a comprehensive review of large-sample results for high-dimensional factor models estimated via dynamic PCA. 6) DSGEs and Factor Models . 8) Empirical Performance of High-Dimensional Methods Dynamic Factor Analysis Models With Time-Varying Parameters. PFAsim Simulated time series data of a multisubject process factor analysis PPsim Simulated time series data for multiple eco-systems based on a predator-and-prey model RSPPsim Simulated time series data for multiple eco-systems based on a regime-switching predator-and-prey model TrueInit_Y14 Simulated multilevel multi-subject time series of a Linear State-Space Models: Dynamic Model it = k + B k i;t 1 + it; (3) k = w k 1 vector of intercepts B k =w k w k regression matrix relating latent variables to each other it = w k 1 vector of residuals or dynamic noise Vectors of xed exogenous variables may be added to the dynamic model (not shown here), but available in the R package dynr. Keywords: dynamic modeling, regime switching, nonlinear, factor analysis, Markov model, state-space model. federici@uniroma1. dsem is an R package for fitting dynamic structural equation models (DSEMs) with a simple user-interface and generic specification of simultaneous and lagged effects in a potentially recursive structure. ). First, contrary to simple dynamic factor analysis where multiple attributes 2. com User Functions Res = dfm(X,X_pred,m,p,frq,isdiff,blocks, threshold, ar_errors, varnames) Main function for estimating dynamic factor models. To make the technique more widely accessible, an introductory guide for DFA dynamic factor model (DFM) is that there are a small number of unobserved common dynamic factors that produce the observed comovements of economic time series. The different steps in the forecasting process and the associated functions within the package are based on the literature. To facilitate economic analysis, it is often convenient to consider a price factor, a nancial market factor, and a labor market factor. Those methods, however, could not estimate ft directly and thus could not be used for forecasting. This is a large topic. You can find the R code for these lecture notes and other related exercises here. , we introduce a dynamic factor model for matrix-valued time series. Apr 20, 2023 · Introduction. Topics for today. Then I will demonstrate how a Dynamic factor analysis. While similar models have been developed in the literature of dynamic factor analysis, our contribution is three-fold. param_names Jan 1, 2009 · Dynamic factor analysis is factor analysis of single-subject multivariate time series. Names of endogenous variables. 51 table d4. Nov 23, 2021 · Dynamic factor models (DFMs), which assume the existence of a small number of unobserved underlying factors common to a large number of variables, are very popular among empirical macroeconomists. Estimation can be done in 3 different ways following: Doz, C. Taking a common example of a demographics based survey, many people will answer questions in a particular ‘way’. data-rich dsge model: summary of the unconditional variance decomposition. Factor Estimation . The Sparse DFM ameliorates interpretability issues of factor structure in classic DFMs by constraining the loading matrices to have few non-zero entries (i. MARSS_TMB. Since the GDPC are based on both leads and lags of the data, like the dynamic principal components defined by Brillinger, they are not May 10, 2018 · Changing Your Viewpoint for Factors In real life, data tends to follow some patterns but the reasons are not apparent right from the start of the data analysis. S. Chapter 10 Dynamic Factor Analysis Here we will use the MARSS package to do Dynamic Factor Analysis (DFA), which allows us to look for a set of common underlying processes among a relatively large set of time series ( Zuur et al. dsem is an R package for fitting dynamic structural equation models (DSEMs) with a simple user-interface and generic specification of simultaneous and lagged effects in a potentially recursive structure. Here we are trying to explain temporal variation in a set of \(n\) observed time series using linear combinations of a set of \(m\) hidden random walks, where \(m << n\). , Giannone, D. Noniterative factor analysis estimators, with algorithms for subset and instrumental variable selection. However, the dimension of F t will in general be different from the dimension of f t since F t includes the leads and lags of 2 Abstract To evaluate the fit of a confirmatory factor analysis model, researchers often rely on fit indices such as SRMR, RMSEA, and CFI. The MARSS() function allows you to fit DFAs with the same form as MARSS(x, form="dfa The implementation is based on efficient C++ code, making dfms orders of magnitude faster than packages such as MARSS that can be used to fit dynamic factor models, or packages like nowcasting and nowcastDFM, which fit dynamic factor models specific to mixed-frequency nowcasting applications. Douglas Thorby, in Structural Dynamics and Vibration in Practice, 2008. With each region corre-sponding to a block, we can distinguish between housing shocks at the regional and the national levels. See full list on cran. it Abstract The aim of the paper is to develop a procedure able to implement Dynamic Factor Analysis (DFA henceforth) in STATA. Jan 16, 2023 · Dynamic factor models are based on the factor analysis model, which assumes that the time series, or observable variables, are generated by a small number of latent factors, plus noise. The latter two packages additionally support Dynamic factors and coincident indices¶. 53 list of figures figure d1. 95, threshold = NULL ) Dec 13, 2021 · Dynamic factor analysis represents a flexible approach for using state-space models to capture latent processes in multivariate time series (Zuur, Fryer, et al. The Linear Single Degree of Freedom System: Response in the Time Domain. r a m , b r o s e , pe t e r, m o l e n a a r Little-V2: “CHAP21” — 2012/9/7 — 09:58 — PAGE 5 — #5 5 Five Steps for Conducting Dynamic Factor Analysis The following sections Details. loglikelihood_burn. Interpretation of results. The dynamic factor is a useful engineering concept that, at its simplest, compares the maximum dynamic displacement response of a system with the static displacement that would be produced by a steady force with the same magnitude Non-Stationary Dynamic Factor Models for Large Datasets Matteo Barigozzi1 Marco Lippi2 Matteo Luciani3 March 8, 2021 Abstract We study a Large-Dimensional Non-Stationary Dynamic Factor Model where (1) the factors Ft are I(1) and singular, that is Ft has dimension r and is driven by q. The aim of the package nowcasting is to offer the tools for the R user to implement dynamic factor models. SEASONAL DYNAMIC FACTOR ANALYSIS (SeaDFA) In this section we present the Seasonal Dynamic Factor Anal ysis, allowing us to deal with common factors following a VARIMA(p, d, q) x (P, D, Q)s model with constant. g volatility clustering, and Apr 11, 2011 · We use the Dynamic Model of Activation proposed by Zautra and colleagues (Zautra, Potter, & Reich, 1997) as a motivating example to construct a dynamic factor model with vector autoregressive We develop a generalized dynamic factor model for panel data with the goal of estimating an unobserved performance index. Rmd. For a given ˆ, the optimal forecast of Y iT+1 at time T is E(Y iT+1jY;ˆ) = ˆY iT + E( ijY;ˆ): In the dynamic panel literature, the focus has been to nd a Closely related to factor analysis is principal component analysis, which creates a picture of the relationships between the variables useful in identifying common factors. Aug 16, 2019 · Nowcasting: An R Package for Predicting Economic Variables Using Dynamic Factor Models. - SAS Procedure, Example Thank you for your help. It can be accessed as follows: May 7, 2010 · 2. Aug 5, 2020 · The dynamic factor model considered in this notebook can be found in the DynamicFactorMQ class, which is a part of the time series analysis component (and in particular the state space models subcomponent) of Statsmodels. , & Reichlin, L. Such an approach requires multivariate time series or state-space models that can model the real-world behavior of nancial markets, e. Constraints for model fitting. ThetraceofAisdenotedbytr(A). It constitutes a generalization of Cattell’s P-technique (Cattell, 1952 ) in that it takes account of lead-lag patterns in the dynamic relationships between latent factor series and observed series. Besides, if restrictions are imposed on C, economic growth can be modelled explicitly by factors. See print() for a discussion of the various output available for marssMLE objects (coefficients, residuals, Kalman filter and smoother output, imputed values for missing data, etc. . Although [R]DSEM is mostly applied to multi-level problems wherein the within- and between-person differences are modeled, here I assume these sources of variations can be disentangled. However it can be "identity", "diagonal and equal", "diagonal and unequal" or a time-varying fixed or estimated diagonal matrix. . It is a method of data reduction that seeks to explain the correlations among many variables in terms of a smaller number of unobservable (latent) variables, known as factors. Indeed, since the 2000’s dynamic factor models have been used extensively to analyze large macroeconomic data sets, sometimes containing hundreds of series with hundreds of observations on each. The aim of the paper is to develop a procedure able to implement Dynamic Factor Analysis (DFA henceforth) in STATA. Factor Estimation The seminal work of Geweke (1977) and Sargent and Sims (1977) used frequency domain methods to look for evidence of a dynamic factor structure and to estimate the importance of the factor. 4 Dynamic factors. 3. endog_names. Empirical analysis using U. The floor function blcreturns the integer part of l. are sparse). Code for today. The seminal work of Geweke (1977) and Sargent and Sims (1977) used frequency domain methods to look for evidence of a dynamic factor structure and to estimate the importance of the factor. The following details what list elements can be passed in: B "Identity". Jan 2, 2023 · Dear SAS Users The data consists only of x and I want to do a Dynamic Factor Analysis I would like to know the concept of Dynamic Factor Analysis and the corresponding SAS Procedure. Note, however, that sparseDFM is an R package for the implementation of popular estimation methods for dynamic factor models (DFMs) including the novel Sparse DFM approach of Mosley et al. regular dsge model: unconditional variance decomposition. 20 April 2023. org This short post notifies you of the CRAN release of a new R package, dfms, to efficiently estimate dynamic factor models in R using the Expectation Maximization (EM) algorithm and Kalman Filtering. 2011. 3 Description Implements Bayesian dynamic factor analysis with 'Stan'. t) is exactly that of the standard factor analysis model | a less-than-full-rank positive de nite matrix plus a diagonal matrix. Dynamic Factor Models: Notation and Summary of Econometric Methods 2. 563697 [Google Scholar] Cudeck R (1991). , 2008). Methods are described in Thorson et al. In fact, it has been shown that the GDPC provide consistent estimates (Smucler 2019) of the common part of dynamic factor models. Multivariate Behavioral Research, 46 (2), 303–339. Usage make_dfa(variables, n_factors, factor_names = paste0("F", seq_len(n_factors))) Arguments variables Character string of variables (i. Learn how to perform dynamic factor analysis using the greta package for R. and . exog_names. jhkim 2. Dynamic factor model is one way to do that by extracting an underlying trend which often follows economic growth pattern. 5 Dynamic Factor Model with 3 trends. Dynamic factor analysis. 8. Maximum likelihood factor analysis programs could therefore be applied to estimate the model, but further simpli cations are possible if we are willing to assume that nis very large and much greater than k, and that r \times r \times T covariance matrices of two-step factor estimates. P_qml: r \times r \times T covariance matrices of QML factor estimates. Nov 18, 2024 · To handle such high-dimensional data, 1 commonly used dimension-reduction technique is factor analysis (FA). The nowcasting package provides the tools to make forecasts of monthly or quarterly economic variables using dynamic factor models. Dynamic factor analysis (DFA) is a technique used to detect common patterns in a set of time series and relationships between these series and explanatory variables. dfms provides a user friendly and computationally efficient approach to estimate linear Gaussian Dynamic Factor Models in R. We then incorporate time-varying volatility and outlier adjustments Feb 2, 2022 · byI n. Factors can be extracted using either nonparametric principal components or parametric Kalman filter and smoothing procedures, with the former being computationally simpler and robust against Jun 22, 2024 · Plot the loadings from a DFA Description. Oct 22, 2022 · In this chapter we deal with linear dynamic factor models and related topics, such as dynamic principal component analysis (dynamic PCA). A very simple model. is dynamic factor analysis (DFA) (Zuur, Fryer, etal. , column names of tsdata). It can be accessed as follows: In the R software factor analysis is implemented by the factanal() function of the build-in stats package. 52 table d5. DFA is an extension of factor analysis for time- series data, and estimates a small number of unobserved processes (‘trends’), that can describe observed data. Introduction The past several decades have seen a signi cant rise in the use of intensive longitudinal May 29, 2024 · The package 'dynr' (Dynamic Modeling in R) is an R package that implements a set of computationally efficient algorithms for handling a broad class of linear and nonlinear discrete- and continuous-time models with regime-switching properties under the constraint of linear Gaussian measurement functions. make_dfa Make text for dynamic factor analysis Description Make the text string for a dynamic factor analysis expressed using arrow-and-lag notation for DSEM. They have proved useful for synthesizing information from variables observed at The implementation is based on efficient C++ code, making dfms orders of magnitude faster than packages such as MARSS that can be used to fit dynamic factor models, or packages like nowcasting and nowcastDFM, which fit dynamic factor models specific to mixed-frequency nowcasting applications. Feb 2, 2019 · About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright A note on model selection Thus, work out fixed effects (covariates) while keeping the random effects (states) constant, and vice versa For example, compare data support for models with different In sum, the availability of software tools and computational power now afford the possibility to conduct person-specific DFA with relative ease and speed. dfactor — Dynamic-factor models DescriptionQuick startMenuSyntax OptionsRemarks and examplesStored resultsMethods and formulas ReferencesAlso see Description dfactor estimates the parameters of dynamic-factor models by maximum likelihood. The names of the exogenous variables. data suggest several (7) dynamic factors, 2. 14/39 Apr 20, 2023 · Dynamic Factor Analysis (DFA) Forms of covariance matrix. 1. A diffusion index is intended to indicate the changes of the fraction of economic data time series which increase or decrease over the selected time interval, For example, housing data are available for di erent regions in the U. r-project. dynamic factor analysis to reduce the dimension of a multivariate dataset, and detecting structural breaks in data sets. 1. (2011). , 2003; Zuur, Tuck, et al. The model argument is a list. Factor Analysis. Here, we highlight how DSEM can be used to implement dynamic factor analysis (DFA). For example, if . Factor analysis is based on various concepts from Linear Algebra, in particular eigenvalues, eigenvectors, orthogonal matrices, and the spectral theorem. doi: 10. initialization. Value. 'bayesdfa' extends conventional dynamic factor models in several ways. Approximate Dynamic Factor Models via the EM algorithm Matteo Barigozzi and Matteo Luciani 2024-086 Please cite this paper as: Barigozzi, Matteo, and Matteo Luciani (2024). dfms is intended to provide a simple, numerically robust, and computationally efficient baseline implementation of (linear Gaussian) Dynamic Factor Models for R, allowing straightforward application to various contexts such as time series dimensionality reduction and multivariate forecasting. (2024) "Dynamic structural equation models synthesize ecosystem dynamics constrained by ecological mechanisms. It is a model of the measurement of a latent variable. Dynamic Factor Analysis FISH 550 – Applied Time Series Analysis Mark Scheuerell. , 2003). TheadjugatematrixofAiswrittenasadj(A). Nov 29, 2019 · where μ i is the mean of x i, λ i is an r × 1 vector, and e it and f t are two uncorrelated processes. io Find an R Examples. The Lorenz equations, the system of differential equations that generate this butterfly-shaped attractor is one example of a dynamical systems model that can be fitted in dynr. 5) Factors as Instruments . fdim uvokxcj oecqiwy thxvvxg tnx fquery xcn syjkwtn wspc dimcgx